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Chapter 7 - Test bank
Business Decision Analysis Tools (Northwest Missouri State University)
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Quantitative Analysis for Management, 13e (Render et al.)
Chapter 7 Linear Programming Models: Graphical and Computer Methods
1) Management resources that need control include machinery usage, labor volume, money
spent, time used, warehouse space used, and material usage.
Answer: TRUE
Diff: Easy
Topic: INTRODUCTION
LO: 7.1: Identify the basic assumptions and properties of linear programming (LP).
AACSB: Analytical thinking
Classification: Concept
2) In the term linear programming, the word programming comes from the phrase "computer
programming."
Answer: FALSE
Diff: Moderate
Topic: INTRODUCTION
LO: 7.1: Identify the basic assumptions and properties of linear programming (LP).
AACSB: Analytical thinking
Classification: Concept
3) One of the assumptions of LP is "simultaneity."
Answer: FALSE
Diff: Moderate
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
LO: 7.1: Identify the basic assumptions and properties of linear programming (LP).
AACSB: Analytical thinking
Classification: Concept
4) Any linear programming problem can be solved using the graphical solution procedure.
Answer: FALSE
Diff: Easy
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Concept
5) An LP formulation typically requires finding the maximum value of an objective while
simultaneously maximizing usage of the resource constraints.
Answer: FALSE
Diff: Moderate
Topic: FORMULATING LP PROBLEMS
LO: 7.2: Formulate a linear programming problem algebraically.
AACSB: Analytical thinking
Classification: Concept
6) There are no limitations on the number of constraints or variables that can be graphed to solve
an LP problem.
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Answer: FALSE
Diff: Easy
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Concept
7) Resource restrictions are called constraints.
Answer: TRUE
Diff: Easy
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
LO: 7.1: Identify the basic assumptions and properties of linear programming (LP).
AACSB: Analytical thinking
Classification: Concept
8) One of the assumptions of LP is "proportionality."
Answer: TRUE
Diff: Moderate
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
LO: 7.1: Identify the basic assumptions and properties of linear programming (LP).
AACSB: Analytical thinking
Classification: Concept
9) The set of solution points that satisfies all of a linear programming problem's constraints
simultaneously is defined as the feasible region in graphical linear programming.
Answer: TRUE
Diff: Moderate
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Concept
10) An objective function is necessary in a maximization problem but is not required in a
minimization problem.
Answer: FALSE
Diff: Easy
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
LO: 7.1: Identify the basic assumptions and properties of linear programming (LP).
AACSB: Analytical thinking
Classification: Concept
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11) In some instances, an infeasible solution may be the optimum found by the corner point
method.
Answer: FALSE
Diff: Moderate
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Concept
12) The rationality assumption implies that solutions need not be in whole numbers (integers).
Answer: FALSE
Diff: Moderate
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
LO: 7.1: Identify the basic assumptions and properties of linear programming (LP).
AACSB: Analytical thinking
Classification: Concept
13) The solution to a linear programming problem must always lie on a constraint.
Answer: TRUE
Diff: Moderate
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Concept
14) In a linear program, the constraints must be linear, but the objective function may be
nonlinear.
Answer: FALSE
Diff: Moderate
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
LO: 7.1: Identify the basic assumptions and properties of linear programming (LP).
AACSB: Analytical thinking
Classification: Concept
15) Resource mix problems use LP to decide how much of each product to make, given a series
of resource restrictions.
Answer: FALSE
Diff: Moderate
Topic: FORMULATING LP PROBLEMS
LO: 7.2: Formulate a linear programming problem algebraically.
AACSB: Analytical thinking
Classification: Concept
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16) The existence of non-negativity constraints in a two-variable linear program implies that we
are always working in the northwest quadrant of a graph.
Answer: FALSE
Diff: Moderate
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Concept
17) The shadow price is the same as the dual price in maximization problems.
Answer: TRUE
Diff: Moderate
Topic: SENSITIVITY ANALYSIS
LO: 7.7: Understand the role of sensitivity analysis.
AACSB: Analytical thinking
Classification: Concept
18) The term slack is associated with ≥ constraints.
Answer: FALSE
Diff: Moderate
Topic: SENSITIVITY ANALYSIS
LO: 7.7: Understand the role of sensitivity analysis.
AACSB: Analytical thinking
Classification: Concept
19) The term surplus is associated with ≥ constraints.
Answer: TRUE
Diff: Moderate
Topic: SENSITIVITY ANALYSIS
LO: 7.7: Understand the role of sensitivity analysis.
AACSB: Analytical thinking
Classification: Concept
20) Any time that we have an isoprofit line that is parallel to a constraint, we have the possibility
of multiple solutions.
Answer: TRUE
Diff: Moderate
Topic: FOUR SPECIAL CASES IN LP
LO: 7.6: Understand special issues in LP such as infeasibility, unboundedness, redundancy, and
alternative optimal solutions.
AACSB: Analytical thinking
Classification: Concept
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21) If the isoprofit line is not parallel to a constraint, then the solution must be unique.
Answer: TRUE
Diff: Moderate
Topic: FOUR SPECIAL CASES IN LP
LO: 7.6: Understand special issues in LP such as infeasibility, unboundedness, redundancy, and
alternative optimal solutions.
AACSB: Analytical thinking
Classification: Concept
22) When two or more constraints conflict with one another, we have a condition called
unboundedness.
Answer: FALSE
Diff: Moderate
Topic: FOUR SPECIAL CASES IN LP
LO: 7.6: Understand special issues in LP such as infeasibility, unboundedness, redundancy, and
alternative optimal solutions.
AACSB: Analytical thinking
Classification: Concept
23) The addition of a redundant constraint lowers the isoprofit line.
Answer: FALSE
Diff: Moderate
Topic: FOUR SPECIAL CASES IN LP
LO: 7.6: Understand special issues in LP such as infeasibility, unboundedness, redundancy, and
alternative optimal solutions.
AACSB: Analytical thinking
Classification: Concept
24) Sensitivity analysis enables us to look at the effects of changing the coefficients in the
objective function, one at a time.
Answer: TRUE
Diff: Moderate
Topic: SENSITIVITY ANALYSIS
LO: 7.7: Understand the role of sensitivity analysis.
AACSB: Analytical thinking
Classification: Concept
25) In a minimization problem, the isocost line is used rather than an isoprofit line.
Answer: TRUE
Diff: Moderate
Topic: SOLVING MINIMIZATION PROBLEMS
LO: 7.5: Understand the difference between minimization and maximization objective
functions.
AACSB: Analytical thinking
Classification: Concept
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26) Unlike a maximization problem, a two-variable minimization problem may not be solved
graphically.
Answer: FALSE
Diff: Easy
Topic: SOLVING MINIMIZATION PROBLEMS
LO: 7.5: Understand the difference between minimization and maximization objective
functions.
AACSB: Analytical thinking
Classification: Concept
27) In a minimization problem, the isocost line slides down and to the left through a feasible
region to reflect decreasing costs.
Answer: TRUE
Diff: Moderate
Topic: SOLVING MINIMIZATION PROBLEMS
LO: 7.5: Understand the difference between minimization and maximization objective
functions.
AACSB: Analytical thinking
Classification: Concept
28) When using Solver to find a solution for an LP problem, both the left-hand side and the
right-hand side of your constraints must be a formula calculated using the cells containing the
decision variables.
Answer: FALSE
Diff: Moderate
Topic: SOLVING FLAIR FURNITURE'S LP PROBLEM USING QM FOR WINDOWS AND
EXCEL 2016 AND EXCEL QM
LO: 7.4: Use Excel spreadsheets to solve LP problems.
AACSB: Analytical thinking
Classification: Concept
29) If you enter inequalities such as "≤" directly into your Excel spreadsheet, you do not need to
designate them when defining constraints using Solver.
Answer: FALSE
Diff: Moderate
Topic: SOLVING FLAIR FURNITURE'S LP PROBLEM USING QM FOR WINDOWS AND
EXCEL 2016 AND EXCEL QM
LO: 7.4: Use Excel spreadsheets to solve LP problems.
AACSB: Analytical thinking
Classification: Concept
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30) Constraints do not need to be entered one at a time when using Solver.
Answer: TRUE
Diff: Easy
Topic: SOLVING FLAIR FURNITURE'S LP PROBLEM USING QM FOR WINDOWS AND
EXCEL 2016 AND EXCEL QM
LO: 7.4: Use Excel spreadsheets to solve LP problems.
AACSB: Analytical thinking
Classification: Concept
31) A widely used mathematical programming technique designed to help managers and decision
making relative to resource allocation is called
A) linear programming.
B) computer programming.
C) constraint programming.
D) goal programming.
Answer: A
Diff: Easy
Topic: INTRODUCTION
LO: 7.1: Identify the basic assumptions and properties of linear programming (LP).
AACSB: Analytical thinking
Classification: Concept
32) Which of the following is not a property of all linear programming problems?
A) the presence of restrictions
B) optimization of some objective
C) a computer program
D) alternate courses of action to choose from
Answer: C
Diff: Moderate
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
LO: 7.1: Identify the basic assumptions and properties of linear programming (LP).
AACSB: Analytical thinking
Classification: Concept
33) A feasible solution to a linear programming problem
A) must be a corner point of the feasible region.
B) must satisfy all of the problem's constraints simultaneously.
C) need not satisfy all of the constraints, only the non-negativity constraints.
D) must give the maximum possible profit.
Answer: B
Diff: Moderate
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Concept
34) Infeasibility in a linear programming problem occurs when
A) a constraint is redundant.
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B) more than one solution is optimal.
C) the feasible region is unbounded.
D) there is no solution that satisfies all the constraints given.
Answer: D
Diff: Moderate
Topic: FOUR SPECIAL CASES IN LP
LO: 7.6: Understand special issues in LP such as infeasibility, unboundedness, redundancy, and
alternative optimal solutions.
AACSB: Analytical thinking
Classification: Concept
35) In a maximization problem, when one or more of the solution variables and the profit can be
made infinitely large without violating any constraints, the linear program has
A) an infeasible solution.
B) an unbounded solution.
C) a redundant constraint.
D) alternate optimal solutions.
Answer: B
Diff: Moderate
Topic: FOUR SPECIAL CASES IN LP
LO: 7.6: Understand special issues in LP such as infeasibility, unboundedness, redundancy, and
alternative optimal solutions.
AACSB: Analytical thinking
Classification: Concept
36) Which of the following is not a part of every linear programming problem formulation?
A) an objective function
B) a set of constraints
C) non-negativity constraints
D) a redundant constraint
Answer: D
Diff: Moderate
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
LO: 7.1: Identify the basic assumptions and properties of linear programming (LP).
AACSB: Analytical thinking
Classification: Concept
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37) When appropriate, the optimal solution to a maximization linear programming problem can
be found by graphing the feasible region and
A) finding the profit at every corner point of the feasible region to see which one gives the
highest value.
B) moving the isoprofit lines towards the origin in a parallel fashion until the last point in the
feasible region is encountered.
C) locating the point that is highest on the graph.
D) sliding the constraints to find the greatest point of intersection.
Answer: A
Diff: Moderate
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Concept
38) The mathematical theory behind linear programming states that an optimal solution to any
problem will lie at a(n) ________ of the feasible region.
A) interior point or center
B) maximum point or minimum point
C) corner point or extreme point
D) interior point or extreme point
Answer: C
Diff: Easy
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Concept
39) Which of the following is not a property of linear programs?
A) one objective function
B) at least two separate feasible regions
C) alternative courses of action
D) one or more constraints
Answer: B
Diff: Easy
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
LO: 7.1: Identify the basic assumptions and properties of linear programming (LP).
AACSB: Analytical thinking
Classification: Concept
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40) The corner point solution method
A) will always provide one, and only one, optimum.
B) will yield different results from the isoprofit line solution method.
C) requires that the profit from all corners of the feasible region be compared.
D) requires that all corners created by all constraints be compared.
Answer: C
Diff: Moderate
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Concept
41) When a constraint line bounding a feasible region has the same slope as an isoprofit line
A) there may be more than one optimum solution.
B) the problem involves redundancy.
C) an error has been made in the problem formulation.
D) a condition of infeasibility exists.
Answer: A
Diff: Moderate
Topic: FOUR SPECIAL CASES IN LP
LO: 7.6: Understand special issues in LP such as infeasibility, unboundedness, redundancy, and
alternative optimal solutions.
AACSB: Analytical thinking
Classification: Concept
42) The simultaneous equation method is
A) an alternative to the corner point method.
B) useful only in minimization methods.
C) an algebraic means for solving the intersection of two or more constraint equations.
D) useful only when more than two product variables exist in a product mix problem.
Answer: C
Diff: Moderate
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Concept
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43) Consider the following linear programming problem:
Maximize
Subject to:
12X + 10Y
4X + 3Y ≤ 480
2X + 3Y ≤ 360
all variable ≥ 0
The maximum possible value for the objective function is
A) 360.
B) 480.
C) 1520.
D) 1560.
Answer: C
Diff: Difficult
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Application
44) Consider the following linear programming problem:
Maximize
Subject to:
4X + 10Y
3X + 4Y ≤ 480
4X + 2Y ≤ 360
all variable ≥ 0
The feasible corner points are (48,84), (0,120), (0,0), (90,0). What is the maximum possible
value for the objective function?
A) 1032
B) 1200
C) 360
D) 1600
Answer: B
Diff: Moderate
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Application
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45) Consider the following linear programming problem:
Maximize
Subject to:
5X + 6Y
4X + 2Y ≤ 420
1X + 2Y ≤ 120
all variable ≥ 0
Which of the following points (X,Y) is not a feasible corner point?
A) (0,60)
B) (105,0)
C) (120,0)
D) (100,10)
Answer: C
Diff: Moderate
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Application
46) Consider the following linear programming problem:
Maximize
Subject to:
5X + 6Y
4X + 2Y ≤ 420
1X + 2Y ≤ 120
all variable ≥ 0
Which of the following points (X,Y) is not feasible?
A) (50,40)
B) (20,50)
C) (60,30)
D) (90,10)
Answer: A
Diff: Moderate
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Application
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47) Two models of a product — Regular (X) and Deluxe (Y) — are produced by a company. A
linear programming model is used to determine the production schedule. The formulation is as
follows:
Maximize profit = 50X + 60Y
Subject to:
8X + 10Y ≤ 800 (labor hours)
X + Y ≤ 120
(total units demanded)
4X + 5Y ≤ 500 (raw materials)
all variable ≥ 0
The optimal solution is X = 100, Y = 0.
How many units of the regular model would be produced based on this solution?
A) 0
B) 100
C) 50
D) 120
Answer: B
Diff: Easy
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Application
48) Two models of a product — Regular (X) and Deluxe (Y) — are produced by a company. A
linear programming model is used to determine the production schedule. The formulation is as
follows:
Maximize profit = 50X + 60Y
Subject to:
8X + 10Y ≤ 800 (labor hours)
X + Y ≤ 120
(total units demanded)
4X + 5Y ≤ 500 (raw materials)
all variable ≥ 0
The optimal solution is X = 100, Y = 0.
Which of these constraints is redundant?
A) the first constraint
B) the second constraint
C) the third constraint
D) the fourth constraint
Answer: B
Diff: Difficult
Topic: FOUR SPECIAL CASES IN LP
LO: 7.6: Understand special issues in LP such as infeasibility, unboundedness, redundancy, and
alternative optimal solutions.
AACSB: Analytical thinking
Classification: Application
49) Consider the following linear programming problem:
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Minimize
Subject to:
20X + 30Y
2X + 4Y ≤ 800
6X + 3Y ≥ 300
X, Y ≥ 0
What is the optimum solution to this problem (X,Y)?
A) (0,0)
B) (50,0)
C) (0,100)
D) (400,0)
Answer: B
Diff: Difficult
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Application
50) Consider the following linear programming problem:
Maximize
Subject to:
20X + 30Y
X + Y ≤ 80
8X + 9Y ≤ 600
3X + 2Y ≥ 400
X, Y ≥ 0
This is a special case of a linear programming problem in which
A) there is no feasible solution.
B) there is a redundant constraint.
C) there are multiple optimal solutions.
D) this cannot be solved graphically.
Answer: A
Diff: Difficult
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Application
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51) Which of the following is not acceptable as a constraint in a linear programming problem
(maximization)?
Constraint 1
Constraint 2
Constraint 3
Constraint 4
X + XY + Y ≥ 12
X - 2Y ≤ 20
X + 3Y = 48
X + Y + Z ≤ 150
A) Constraint 1
B) Constraint 2
C) Constraint 3
D) Constraint 4
Answer: A
Diff: Moderate
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
LO: 7.1: Identify the basic assumptions and properties of linear programming (LP).
AACSB: Analytical thinking
Classification: Application
52) If one changes the contribution rates in the objective function of an LP
A) the feasible region will change.
B) the slope of the isoprofit or isocost line will change.
C) the optimal solution to the LP is sure to no longer be optimal.
D) the problem will no longer be linear.
Answer: B
Diff: Moderate
Topic: SENSITIVITY ANALYSIS
LO: 7.7: Understand the role of sensitivity analysis.
AACSB: Analytical thinking
Classification: Concept
53) Sensitivity analysis may also be called
A) postoptimality analysis.
B) nonparametric programming.
C) preoptimality analysis.
D) redundancy testing
Answer: A
Diff: Moderate
Topic: SENSITIVITY ANALYSIS
LO: 7.7: Understand the role of sensitivity analysis.
AACSB: Analytical thinking
Classification: Concept
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54) Sensitivity analyses are used to examine the effects of changes in
A) contribution rates for each variable.
B) degree space.
C) the modeler.
D) the degrees of freedom in the numerator
Answer: A
Diff: Moderate
Topic: SENSITIVITY ANALYSIS
LO: 7.7: Understand the role of sensitivity analysis.
AACSB: Analytical thinking
Classification: Concept
55) Which of the following is a basic assumption of linear programming?
A) The condition of uncertainty exists.
B) Independence exists for the activities.
C) Proportionality exists in the objective function and constraints.
D) Divisibility does not exist, allowing only integer solutions.
Answer: C
Diff: Moderate
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
LO: 7.1: Identify the basic assumptions and properties of linear programming (LP).
AACSB: Analytical thinking
Classification: Concept
56) If the addition of a constraint to a linear programming problem does not change the solution,
the constraint is said to be
A) unbounded.
B) non-negative.
C) infeasible.
D) redundant.
Answer: D
Diff: Moderate
Topic: FOUR SPECIAL CASES IN LP
LO: 7.6: Understand special issues in LP such as infeasibility, unboundedness, redundancy, and
alternative optimal solutions.
AACSB: Analytical thinking
Classification: Concept
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57) Which of the following is not an assumption of LP?
A) simultaneity
B) certainty
C) proportionality
D) divisibility
Answer: A
Diff: Moderate
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
LO: 7.1: Identify the basic assumptions and properties of linear programming (LP).
AACSB: Analytical thinking
Classification: Concept
58) The difference between the left-hand side and right-hand side of a less-than-or-equal-to
constraint is referred to as
A) surplus.
B) constraint.
C) slack.
D) shadow price.
Answer: C
Diff: Moderate
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Concept
59) The difference between the left-hand side and right-hand side of a greater-than-or-equal-to
constraint is referred to as
A) surplus.
B) constraint.
C) slack.
D) shadow price.
Answer: A
Diff: Moderate
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Concept
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60) A constraint with zero slack or surplus is called a
A) nonbinding constraint.
B) resource constraint.
C) binding constraint.
D) nonlinear constraint.
Answer: C
Diff: Easy
Topic: SOLVING FLAIR FURNITURE'S LP PROBLEM USING QM FOR WINDOWS AND
EXCEL 2016 AND EXCEL QM
LO: 7.4: Use Excel spreadsheets to solve LP problems.
AACSB: Analytical thinking
Classification: Concept
61) The coefficients of the variables in the constraint equations that represent the amount of
resources needed to produce one unit of the variable are called
A) technological coefficients.
B) objective coefficients.
C) shadow prices.
D) dual prices.
Answer: A
Diff: Moderate
Topic: SENSITIVITY ANALYSIS
LO: 7.7: Understand the role of sensitivity analysis.
AACSB: Analytical thinking
Classification: Concept
62) A constraint with positive slack or surplus is called a
A) nonbinding constraint.
B) resource constraint.
C) binding constraint.
D) nonlinear constraint.
Answer: A
Diff: Easy
Topic: SOLVING FLAIR FURNITURE'S LP PROBLEM USING QM FOR WINDOWS AND
EXCEL 2016 AND EXCEL QM
LO: 7.4: Use Excel spreadsheets to solve LP problems.
AACSB: Analytical thinking
Classification: Concept
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63) A straight line representing all non-negative combinations of X1 and X2 for a particular
profit level is called a(n)
A) objective line.
B) sensitivity line.
C) profit line.
D) isoprofit line.
Answer: D
Diff: Moderate
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Concept
64) In order for a linear programming problem to have a unique solution, the solution must exist
A) at the intersection of the non-negativity constraints.
B) at the intersection of a non-negativity constraint and a resource constraint.
C) at the intersection of the objective function and a constraint.
D) at the intersection of two or more constraints.
Answer: D
Diff: Moderate
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Concept
65) In order for a linear programming problem to have multiple solutions, the solution must exist
A) at the intersection of the non-negativity constraints.
B) on a non-redundant constraint parallel to the objective function.
C) at the intersection of the objective function and a constraint.
D) at the intersection of three or more constraints.
Answer: B
Diff: Moderate
Topic: FOUR SPECIAL CASES IN LP
LO: 7.6: Understand special issues in LP such as infeasibility, unboundedness, redundancy, and
alternative optimal solutions.
AACSB: Analytical thinking
Classification: Concept
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66) Consider the following linear programming problem:
Maximize
Subject to:
12X + 10Y
4X + 3Y ≤ 480
2X + 3Y ≤ 360
all variables ≥ 0
Which of the following points (X,Y) is feasible?
A) (10,120)
B) (120,10)
C) (30,100)
D) (60,90)
Answer: C
Diff: Moderate
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Application
67) Consider the following linear programming problem:
Maximize
Subject to:
5X + 6Y
4X + 2Y ≤ 420
1X + 2Y ≤ 120
all variables ≥ 0
Which of the following points (X,Y) is in the feasible region?
A) (30,60)
B) (105,5)
C) (0,210)
D) (100,10)
Answer: D
Diff: Moderate
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Application
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68) Consider the following linear programming problem:
Maximize
Subject to:
5X + 6Y
4X + 2Y ≤ 420
1X + 2Y ≤ 120
all variables ≥ 0
Which of the following points (X,Y) is feasible?
A) (50,40)
B) (30,50)
C) (60,30)
D) (90,20)
Answer: C
Diff: Moderate
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Application
69) Which of the following is not an assumption of LP?
A) certainty
B) proportionality
C) divisibility
D) multiplicativity
Answer: D
Diff: Moderate
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
LO: 7.1: Identify the basic assumptions and properties of linear programming (LP).
AACSB: Analytical thinking
Classification: Concept
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70) Consider the following linear programming problem:
Maximize
Subject to:
20X + 30Y
X + Y ≤ 80
12X + 12Y ≤ 600
3X + 2Y ≤ 400
X, Y ≥ 0
This is a special case of a linear programming problem in which
A) there is no feasible solution.
B) there is a redundant constraint.
C) there are multiple optimal solutions.
D) this cannot be solved graphically.
Answer: B
Diff: Difficult
Topic: FOUR SPECIAL CASES IN LP
LO: 7.6: Understand special issues in LP such as infeasibility, unboundedness, redundancy, and
alternative optimal solutions.
AACSB: Analytical thinking
Classification: Concept
71) Which of the following functions is not linear?
A) 5X + 3Z
B) 3X + 4Y + Z - 3
C) 2X + 5YZ
D) Z
Answer: C
Diff: Easy
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
LO: 7.1: Identify the basic assumptions and properties of linear programming (LP).
AACSB: Analytical thinking
Classification: Application
72) Which of the following is not one of the steps in formulating a linear program?
A) Graph the constraints to determine the feasible region.
B) Define the decision variables.
C) Use the decision variables to write mathematical expressions for the objective function and
the constraints.
D) Identify the objective and the constraints.
Answer: A
Diff: Moderate
Topic: FORMULATING LP PROBLEMS
LO: 7.2: Formulate a linear programming problem algebraically.
AACSB: Analytical thinking
Classification: Concept
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73) What type of problems use LP to decide how much of each product to make, given a series
of resource restrictions?
A) resource mix
B) product restriction
C) resource allocation
D) product mix
Answer: D
Diff: Moderate
Topic: FORMULATING LP PROBLEMS
LO: 7.2: Formulate a linear programming problem algebraically.
AACSB: Analytical thinking
Classification: Concept
Consider the sensitivity report below for the problems which follow.
74) The optimal solution to this linear program is
A) x1 = 34, x2 = 40.
B) x1 = 6, x2 = 11.
C) x1 = 7.33, x2 = 6.
D) x1 = 3, x2 = 6.
Answer: D
Diff: Easy
Topic: SENSITIVITY ANALYSIS
LO: 7.7: Understand the role of sensitivity analysis.
AACSB: Analytical thinking
Classification: Application
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75) Which of the following constraints are binding?
A) Extrusion only
B) Packing only
C) Additive only
D) Extrusion and Packaging
Answer: D
Diff: Moderate
Topic: SENSITIVITY ANALYSIS
LO: 7.7: Understand the role of sensitivity analysis.
AACSB: Analytical thinking
Classification: Concept
76) What is the increase in the objective value if 2 units of extrusion are added?
A) 3
B) 6
C) 48
D) 96
Answer: B
Diff: Moderate
Topic: SENSITIVITY ANALYSIS
LO: 7.7: Understand the role of sensitivity analysis.
AACSB: Analytical thinking
Classification: Application
77) What is the increase in the objective value if 2 units of packaging are added?
A) 11
B) 18
C) 22
D) 36
Answer: C
Diff: Moderate
Topic: SENSITIVITY ANALYSIS
LO: 7.7: Understand the role of sensitivity analysis.
AACSB: Analytical thinking
Classification: Application
78) What is the increase in the objective value if 2 units of additive are added?
A) 0
B) 4
C) 12
D) 16
Answer: A
Diff: Moderate
Topic: SENSITIVITY ANALYSIS
LO: 7.7: Understand the role of sensitivity analysis.
AACSB: Analytical thinking
Classification: Application
79) Consider the following linear programming problem:
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Maximize
Subject to:
10X + 30Y
X + 2Y ≤ 80
8X + 16Y ≤ 640
4X + 2Y ≥ 100
X, Y ≥ 0
This is a special case of a linear programming problem in which
A) there is no feasible solution.
B) there is a redundant constraint.
C) there are multiple optimal solutions.
D) this cannot be solved graphically.
Answer: B
Diff: Difficult
Topic: FOUR SPECIAL CASES IN LP
LO: 7.6: Understand special issues in LP such as infeasibility, unboundedness, redundancy, and
alternative optimal solutions.
AACSB: Analytical thinking
Classification: Application
80) Consider the following constraints from a linear programming problem:
2X + Y ≤ 200
X + 2Y ≤ 200
X, Y ≥ 0
If these are the only constraints, which of the following points (X,Y) cannot be the optimal
solution?
A) (0, 0)
B) (0, 200)
C) (0,100)
D) (100, 0)
Answer: B
Diff: Difficult
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Application
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lOMoARcPSD|18541965
81) Consider the following constraints from a linear programming problem:
2X + Y ≤ 200
X + 2Y ≤ 200
X, Y ≥ 0
If these are the only constraints, which of the following points (X,Y) cannot be the optimal
solution?
A) (0, 0)
B) (0, 100)
C) (65, 65)
D) (100, 0)
Answer: C
Diff: Difficult
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Application
82) Classic New Orleans desserts include pralines, pecan pie and Bananas Foster — all three are
absolutely essential to eat on any trip to the city. Chefs may quibble about this ingredient list as
there are dozens of variations on each recipe, but these ingredients are common to most
formulations. A recipe for a dozen pralines takes a cup of pecans, two cups of brown sugar, a cup
of granulated sugar, a half teaspoon of vanilla and a tablespoon of rum. A pecan pie takes two
cups of pecans, a cup of brown sugar, a cup of cane syrup, a cup of granulated sugar, a teaspoon
of vanilla, and a tablespoon of rum. A recipe for Bananas Foster requires a cup of pecans, a cup
of brown sugar, a cup of granulated sugar, a banana, and a tablespoon of rum and makes two
servings. Bananas Foster is considered a dessert for two and is priced accordingly at $15. Your
pantry has on hand 24 cups of pecans, 40 cups of brown sugar, 12 cups of cane syrup, 20 cups of
granulated sugar, 40 teaspoons of vanilla, twelve bananas, and 64 tablespoons of rum. Pralines
sell for $22.68 per dozen and a pecan pie costs $22.40. Which of these is an appropriate
objective function?
A) Max Z = $7.5BF + $11.34Pr + $11.20Pe
B) Max Z = $15BF + $22.68Pr 9 $22.40Pe
C) Max Z = $7.5BF + $22.68Pr + $22.40Pe
D) Max Z = $15BF + $11.34Pr + $11.20Pe
Answer: B
Diff: Moderate
Topic: FORMULATING LP PROBLEMS
LO: 7.2: Formulate a linear programming problem algebraically.
AACSB: Analytical thinking
Classification: Application
Downloaded by ??c V? (ducvu0712@gmail.com)
lOMoARcPSD|18541965
83) Classic New Orleans desserts include pralines, pecan pie and Bananas Foster — all three are
absolutely essential to eat on any trip to the city. Chefs may quibble about this ingredient list as
there are dozens of variations on each recipe, but these ingredients are common to most
formulations. A recipe for a dozen pralines takes a cup of pecans, two cups of brown sugar, a cup
of granulated sugar, a half teaspoon of vanilla and a tablespoon of rum. A pecan pie takes two
cups of pecans, a cup of brown sugar, a cup of cane syrup, a cup of granulated sugar, a teaspoon
of vanilla, and a tablespoon of rum. A recipe for Bananas Foster requires a cup of pecans, a cup
of brown sugar, a cup of granulated sugar, a banana, and a tablespoon of rum and makes two
servings. Bananas Foster is considered a dessert for two and is priced accordingly at $15. Your
pantry has on hand 24 cups of pecans, 40 cups of brown sugar, 12 cups of cane syrup, 20 cups of
granulated sugar, 40 teaspoons of vanilla, twelve bananas, and 64 tablespoons of rum. Pralines
sell for $22.68 per dozen and a pecan pie costs $22.40. Which of these is an appropriate
constraint?
A) 1Pr + 2Pe + 1BF ≤ 24
B) 1Pr + 2Pe + 1BF ≤ 40
C) Pe ≤ 24
D) 1BF ≤ 40
Answer: A
Diff: Moderate
Topic: FORMULATING LP PROBLEMS
LO: 7.2: Formulate a linear programming problem algebraically.
AACSB: Analytical thinking
Classification: Application
84) Classic New Orleans desserts include pralines, pecan pie and Bananas Foster — all three are
absolutely essential to eat on any trip to the city. Chefs may quibble about this ingredient list as
there are dozens of variations on each recipe, but these ingredients are common to most
formulations. A recipe for a dozen pralines takes a cup of pecans, two cups of brown sugar, a cup
of granulated sugar, a half teaspoon of vanilla and a tablespoon of rum. A pecan pie takes two
cups of pecans, a cup of brown sugar, a cup of cane syrup, a cup of granulated sugar, a teaspoon
of vanilla, and a tablespoon of rum. A recipe for Bananas Foster requires a cup of pecans, a cup
of brown sugar, a cup of granulated sugar, a banana, and a tablespoon of rum and makes two
servings. Bananas Foster is considered a dessert for two and is priced accordingly at $15. Your
pantry has on hand 24 cups of pecans, 40 cups of brown sugar, 12 cups of cane syrup, 20 cups of
granulated sugar, 40 teaspoons of vanilla, twelve bananas, and 64 tablespoons of rum. Pralines
sell for $22.68 per dozen and a pecan pie costs $22.40. Which of these is an appropriate
constraint?
A) 1Pr + 2Pe + 1BF ≤ 40
B) 2Pr + 1Pe + 1BF ≤ 24
C) Pe ≤ 12
D) 1BF ≤ 40
Answer: C
Diff: Moderate
Topic: FORMULATING LP PROBLEMS
LO: 7.2: Formulate a linear programming problem algebraically.
AACSB: Analytical thinking
Classification: Application
85) Classic New Orleans desserts include pralines, pecan pie and Bananas Foster — all three are
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lOMoARcPSD|18541965
absolutely essential to eat on any trip to the city. Chefs may quibble about this ingredient list as
there are dozens of variations on each recipe, but these ingredients are common to most
formulations. A recipe for a dozen pralines takes a cup of pecans, two cups of brown sugar, a cup
of granulated sugar, a half teaspoon of vanilla and a tablespoon of rum. A pecan pie takes two
cups of pecans, a cup of brown sugar, a cup of cane syrup, a cup of granulated sugar, a teaspoon
of vanilla, and a tablespoon of rum. A recipe for Bananas Foster requires a cup of pecans, a cup
of brown sugar, a cup of granulated sugar, a banana, and a tablespoon of rum and makes two
servings. Bananas Foster is considered a dessert for two and is priced accordingly at $15. Your
pantry has on hand 24 cups of pecans, 40 cups of brown sugar, 12 cups of cane syrup, 20 cups of
granulated sugar, 40 teaspoons of vanilla, twelve bananas, and 64 tablespoons of rum. Pralines
sell for $22.68 per dozen and a pecan pie costs $22.40. Which of these is an appropriate
constraint?
A) 1Pr + 2Pe + 1BF ≤ 40
B) 2Pr + 1Pe + 1BF ≤ 24
C) Pe ≥ 12
D) BF ≥ 0
Answer: D
Diff: Moderate
Topic: FORMULATING LP PROBLEMS
LO: 7.2: Formulate a linear programming problem algebraically.
AACSB: Analytical thinking
Classification: Application
Downloaded by ??c V? (ducvu0712@gmail.com)
lOMoARcPSD|18541965
86) Classic New Orleans desserts include pralines and Bananas Foster — both are absolutely
essential to eat on any trip to the city. Chefs may quibble about this ingredient list as there are
dozens of variations on each recipe, but these ingredients are common to most formulations. A
recipe for a dozen pralines takes a cup of pecans, two cups of brown sugar, a cup of granulated
sugar, a half teaspoon of vanilla and a tablespoon of rum. A recipe for Bananas Foster requires a
cup of pecans, a cup of brown sugar, a cup of granulated sugar, a banana, and a tablespoon of
rum and makes two servings. Bananas Foster is considered a dessert for two and is priced
accordingly at $15. Your pantry has on hand 24 cups of pecans, 40 cups of brown sugar, 12 cups
of cane syrup, 20 cups of granulated sugar, 40 teaspoons of vanilla, twelve bananas, and 64
tablespoons of rum. Pralines sell for $22.68 per dozen. Your first constraint for a graphical
solution has been plotted. Which constraint is it?
A) the Praline constraint
B) the Bananas Foster constraint
C) the pecan constraint
D) the brown sugar constraint
Answer: D
Diff: Moderate
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Application
Downloaded by ??c V? (ducvu0712@gmail.com)
lOMoARcPSD|18541965
87) Classic New Orleans desserts include pralines and Bananas Foster — both are absolutely
essential to eat on any trip to the city. Chefs may quibble about this ingredient list as there are
dozens of variations on each recipe, but these ingredients are common to most formulations. A
recipe for a dozen pralines takes a cup of pecans, two cups of brown sugar, a cup of granulated
sugar, a half teaspoon of vanilla and a tablespoon of rum. A recipe for Bananas Foster requires a
cup of pecans, a cup of brown sugar, a cup of granulated sugar, a banana, and a tablespoon of
rum and makes two servings. Bananas Foster is considered a dessert for two and is priced
accordingly at $15. Your pantry has on hand 24 cups of pecans, 40 cups of brown sugar, 12 cups
of cane syrup, 20 cups of granulated sugar, 40 teaspoons of vanilla, twelve bananas, and 64
tablespoons of rum. Pralines sell for $22.68 per dozen. Your first constraint for a graphical
solution has been plotted. Which constraint is it?
A) the Praline constraint
B) the Bananas Foster constraint
C) the pecan constraint
D) the brown sugar constraint
Answer: C
Diff: Moderate
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Application
Downloaded by ??c V? (ducvu0712@gmail.com)
lOMoARcPSD|18541965
Classic New Orleans desserts include pralines, pecan pie and Bananas Foster — all three are
absolutely essential to eat on any trip to the city. Chefs may quibble about this ingredient list as
there are dozens of variations on each recipe, but these ingredients are common to most
formulations. A recipe for a dozen pralines takes a cup of pecans, two cups of brown sugar, a cup
of granulated sugar, a half teaspoon of vanilla and a tablespoon of rum. A pecan pie takes two
cups of pecans, a cup of brown sugar, a cup of cane syrup, a cup of granulated sugar, a teaspoon
of vanilla, and a tablespoon of rum. A recipe for Bananas Foster requires a cup of pecans, a cup
of brown sugar, a cup of granulated sugar, a banana, and a tablespoon of rum and makes two
servings. Bananas Foster is considered a dessert for two and is priced accordingly at $15. Your
pantry has on hand 24 cups of pecans, 40 cups of brown sugar, 12 cups of cane syrup, 20 cups of
granulated sugar, 40 teaspoons of vanilla, twelve bananas, and 64 tablespoons of rum. Pralines
sell for $22.68 per dozen and a pecan pie costs $22.40. The Sensitivity Report from an Excel
formulation of this problem is show below.
88) What is the most you would pay for one more cup of brown sugar?
A) $0
B) $0.28
C) $$0.12
D) $0.40
Answer: B
Diff: Moderate
Topic: SENSITIVITY ANALYSIS
LO: 7.7: Understand the role of sensitivity analysis.
AACSB: Analytical thinking
Classification: Application
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lOMoARcPSD|18541965
89) What is the most you would pay for one more cup of pecans?
A) $0
B) $0.20
C) $$0.24
D) $0.40
Answer: A
Diff: Moderate
Topic: SENSITIVITY ANALYSIS
LO: 7.7: Understand the role of sensitivity analysis.
AACSB: Analytical thinking
Classification: Application
90) You don't use any of the
A) pecans.
B) rum.
C) cane syrup.
D) vanilla.
Answer: C
Diff: Moderate
Topic: SENSITIVITY ANALYSIS
LO: 7.7: Understand the role of sensitivity analysis.
AACSB: Analytical thinking
Classification: Application
91) You can actually take in $453.60 with this setup. If you had only one more cup of granulated
sugar what could your profit be?
A) $453.60
B) $454.73
C) $473.60
D) $475.72
Answer: D
Diff: Moderate
Topic: SENSITIVITY ANALYSIS
LO: 7.7: Understand the role of sensitivity analysis.
AACSB: Analytical thinking
Classification: Application
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lOMoARcPSD|18541965
92) You can actually take in $453.60 with this setup. Suppose your most important customer
comes to you and demands you make her an order of Bananas Foster. What is your profit if you
add one recipe of Bananas Foster to your production mix?
A) $446.20
B) $453.60
C) $461.00
D) $473.60
Answer: D
Diff: Moderate
Topic: SENSITIVITY ANALYSIS
LO: 7.7: Understand the role of sensitivity analysis.
AACSB: Analytical thinking
Classification: Application
93) A furniture company is producing two types of furniture. Product A requires 8 board feet of
wood and 2 lbs of wicker. Product B requires 6 board feet of wood and 6 lbs of wicker. There are
2000 board feet of wood available for product and 1000 lbs of wicker. Product A earns a profit
margin of $30 a unit and Product B earns a profit margin of $40 a unit. What should the
objective function be?
A) Maximize 30A + 40B
B) Maximize 10A + 12B
C) Maximize 14Wood + 8Wicker
D) Maximize 8A + 2A + 6B + 6B
Answer: A
Diff: Moderate
Topic: FORMULATING LP PROBLEMS
LO: 7.2: Formulate a linear programming problem algebraically.
AACSB: Analytical thinking
Classification: Application
94) A furniture company is producing two types of furniture. Product A requires 8 board feet of
wood and 2 lbs of wicker. Product B requires 6 board feet of wood and 6 lbs of wicker. There are
2000 board feet of wood available for product and 1000 lbs of wicker. Product A earns a profit
margin of $30 a unit and Product B earns a profit margin of $40 a unit. Which of these is an
appropriate constraint for Wicker?
A) 30A + 40B ≤ 1000
B) 10A + 12B ≤ 1000
C) 8A + 2B ≤ 1000
D) 2A + 6B ≤ 1000
Answer: D
Diff: Moderate
Topic: FORMULATING LP PROBLEMS
LO: 7.2: Formulate a linear programming problem algebraically.
AACSB: Analytical thinking
Classification: Application
Downloaded by ??c V? (ducvu0712@gmail.com)
lOMoARcPSD|18541965
95) A furniture company is producing two types of furniture. Product A requires 8 board feet of
wood and 2 lbs of wicker. Product B requires 6 board feet of wood and 6 lbs of wicker. There are
2000 board feet of wood available for product and 1000 lbs of wicker. Product A earns a profit
margin of $30 a unit and Product B earns a profit margin of $40 a unit. Which of these is an
appropriate constraint for Wood?
A) 30A + 40B ≤ 2000
B) 8A + 6B ≤ 2000
C) 8A + 2B ≤ 2000
D) 2A + 6B ≤ 2000
Answer: B
Diff: Moderate
Topic: FORMULATING LP PROBLEMS
LO: 7.2: Formulate a linear programming problem algebraically.
AACSB: Analytical thinking
Classification: Application
96) As a supervisor of a production department, you must decide the daily production totals of a
certain product that has two models, the Deluxe and the Special. The profit on the Deluxe model
is $12 per unit and the Special's profit is $10. Each model goes through two phases in the
production process, and there are only 100 hours available daily at the construction stage and
only 80 hours available at the finishing and inspection stage. Each Deluxe model requires 20
minutes of construction time and 10 minutes of finishing and inspection time. Each Special
model requires 15 minutes of construction time and 15 minutes of finishing and inspection time.
The company has also decided that the Special model must comprise at least 40 percent of the
production total. What is an appropriate objective function?
A) Maximize 2D + 2.5S
B) Maximize 12D + 10S
C) Maximize 4D + 2.5S
D) Maximize 100D + 80S
Answer: B
Diff: Moderate
Topic: FORMULATING LP PROBLEMS
LO: 7.2: Formulate a linear programming problem algebraically.
AACSB: Analytical thinking
Classification: Application
Downloaded by ??c V? (ducvu0712@gmail.com)
lOMoARcPSD|18541965
97) As a supervisor of a production department, you must decide the daily production totals of a
certain product that has two models, the Deluxe and the Special. The profit on the Deluxe model
is $12 per unit and the Special's profit is $10. Each model goes through two phases in the
production process, and there are only 100 hours available daily at the construction stage and
only 80 hours available at the finishing and inspection stage. Each Deluxe model requires 20
minutes of construction time and 10 minutes of finishing and inspection time. Each Special
model requires 15 minutes of construction time and 15 minutes of finishing and inspection time.
The company has also decided that the Special model must comprise at least 40 percent of the
production total. What is an appropriate constraint for the construction time?
A) 20D + 15S ≥ 6000
B) 20D + 15S ≤ 100
C) 20D + 15S ≤ 6000
D) 20D + 15S ≥ 100
Answer: C
Diff: Moderate
Topic: FORMULATING LP PROBLEMS
LO: 7.2: Formulate a linear programming problem algebraically.
AACSB: Analytical thinking
Classification: Application
98) As a supervisor of a production department, you must decide the daily production totals of a
certain product that has two models, the Deluxe and the Special. The profit on the Deluxe model
is $12 per unit and the Special's profit is $10. Each model goes through two phases in the
production process, and there are only 100 hours available daily at the construction stage and
only 80 hours available at the finishing and inspection stage. Each Deluxe model requires 20
minutes of construction time and 10 minutes of finishing and inspection time. Each Special
model requires 15 minutes of construction time and 15 minutes of finishing and inspection time.
The company has also decided that the Special model must comprise at least 40 percent of the
production total. What is an appropriate constraint for the finishing time?
A) 10D + 15S ≤ 4800
B) 10D + 15S ≥ 100
C) 10D + 15S ≤ 80
D) 15D + 10S ≥ 100
Answer: C
Diff: Moderate
Topic: FORMULATING LP PROBLEMS
LO: 7.2: Formulate a linear programming problem algebraically.
AACSB: Analytical thinking
Classification: Application
Downloaded by ??c V? (ducvu0712@gmail.com)
lOMoARcPSD|18541965
99) As a supervisor of a production department, you must decide the daily production totals of a
certain product that has two models, the Deluxe and the Special. The profit on the Deluxe model
is $12 per unit and the Special's profit is $10. Each model goes through two phases in the
production process, and there are only 100 hours available daily at the construction stage and
only 80 hours available at the finishing and inspection stage. Each Deluxe model requires 20
minutes of construction time and 10 minutes of finishing and inspection time. Each Special
model requires 15 minutes of construction time and 15 minutes of finishing and inspection time.
The company has also decided that the Special model must comprise at least 40 percent of the
production total. The optimal product mix should include
A) 120D's.
B) 120S's.
C) 200D's.
D) 200S's.
Answer: A
Diff: Moderate
Topic: FORMULATING LP PROBLEMS
LO: 7.2: Formulate a linear programming problem algebraically.
AACSB: Analytical thinking
Classification: Application
100) Consider the following linear program.
Maximize
Subject to:
30X + 10Y
3X + Y ≤ 300
X + Y ≤ 200
X ≤ 100
Y ≥ 50
X,Y ≥ 0
Which of these is NOT a corner point of the feasible region?
A) (0,50)
B) (50,50)
C) (50,150)
D) (75,50)
Answer: D
Diff: Difficult
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Application
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lOMoARcPSD|18541965
101) Consider the following linear program:
Maximize
Subject to:
30X + 10Y
3X + Y ≤ 300
X + Y ≤ 200
X ≤ 100
Y ≥ 50
X,Y ≥ 0
What is the optimal solution?
A) $3,000
B) $3,200
C) $3,400
D) $3,600
Answer: A
Diff: Difficult
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Application
102) The Greatest Generation Food Company wishes to introduce a new brand of pureed readyto-eat meals (composed of pureed chicken and pureed liver meat products) that meets certain
nutritional requirements. The liver-flavored product contains 1 unit of nutrient A and 2 units of
nutrient B, while the chicken-flavored product contains 1 unit of nutrient A and 4 units of
nutrient B. According to federal requirements, there must be at least 40 units of nutrient A and
60 units of nutrient B in a package of the new meals. In addition, the company has decided that
there can be no more than 15 units of liver-flavored meat product in a package. It costs 1 cent to
make a liver-flavored product and 2 cents to make a chicken-flavored product. What is an
appropriate objective function for this scenario?
A) Minimize L + 2C
B) Maximize L + 2C
C) Minimize L + C
D) Maximize L + C
Answer: A
Diff: Moderate
Topic: FORMULATING LP PROBLEMS
LO: 7.2: Formulate a linear programming problem algebraically.
AACSB: Analytical thinking
Classification: Application
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lOMoARcPSD|18541965
103) The Greatest Generation Food Company wishes to introduce a new brand of pureed readyto-eat meals (composed of pureed chicken and pureed liver meat products) that meets certain
nutritional requirements. The liver-flavored product contains 1 unit of nutrient A and 2 units of
nutrient B, while the chicken-flavored product contains 1 unit of nutrient A and 4 units of
nutrient B. According to federal requirements, there must be at least 40 units of nutrient A and
60 units of nutrient B in a package of the new meals. In addition, the company has decided that
there can be no more than 15 units of liver-flavored meat product in a package. It costs 1 cent to
make a liver-flavored product and 2 cents to make a chicken-flavored product. Are there any
redundant constraints in this scenario?
A) L + C ≤ 100
B) L + 2C ≥ 40
C) Minimize 2L + 4C ≥ 60
D) There are no redundant constraints.
Answer: C
Diff: Difficult
Topic: FORMULATING LP PROBLEMS
LO: 7.2: Formulate a linear programming problem algebraically.
AACSB: Analytical thinking
Classification: Application
104) The Greatest Generation Food Company wishes to introduce a new brand of pureed readyto-eat meals (composed of pureed chicken and pureed liver meat products) that meets certain
nutritional requirements. The liver-flavored product contains 1 unit of nutrient A and 2 units of
nutrient B, while the chicken-flavored product contains 1 unit of nutrient A and 4 units of
nutrient B. According to federal requirements, there must be at least 40 units of nutrient A and
60 units of nutrient B in a package of the new meals. In addition, the company has decided that
there can be no more than 15 units of liver-flavored meat product in a package. It costs 1 cent to
make a liver-flavored product and 2 cents to make a chicken-flavored product. What is the
minimum cost?
A) 65 cents
B) 70 cents
C) 75 cents
D) 80 cents
Answer: A
Diff: Difficult
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Application
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lOMoARcPSD|18541965
105) The Greatest Generation Food Company wishes to introduce a new brand of pureed readyto-eat meals (composed of pureed chicken and pureed liver meat products) that meets certain
nutritional requirements. The liver-flavored product contains 1 unit of nutrient A and 2 units of
nutrient B, while the chicken-flavored product contains 1 unit of nutrient A and 4 units of
nutrient B. According to federal requirements, there must be at least 40 units of nutrient A and
60 units of nutrient B in a package of the new meals. In addition, the company has decided that
there can be no more than 15 units of liver-flavored meat product in a package. It costs 1 cent to
make a liver-flavored product and 2 cents to make a chicken-flavored product. At what point
does the optimal solution exist?
A) (30,0)
B) (0,40)
C) (15,25)
D) (0,0)
Answer: C
Diff: Difficult
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Application
106) A furniture company is producing two types of furniture. Product A requires 8 board feet of
wood and 2 lbs of wicker. Product B requires 6 board feet of wood and 6 lbs of wicker. There are
2000 board feet of wood available for product and 1000 lbs of wicker. Product A earns a profit
margin of $30 a unit and Product B earns a profit margin of $40 a unit. Formulate the problem as
a linear program.
Answer: Let X1 = number of units of Product A
X2 = number of units of Product B
Maximize
Subject to:
30X1 + 40X2
8X1 + 6X2 ≤ 2000
2X1 + 6X2 ≤ 1000
X1, X2 ≥ 0
Diff: Moderate
Topic: FORMULATING LP PROBLEMS
LO: 7.2: Formulate a linear programming problem algebraically.
AACSB: Analytical thinking
Classification: Application
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107) As a supervisor of a production department, you must decide the daily production totals of a
certain product that has two models, the Deluxe and the Special. The profit on the Deluxe model
is $12 per unit and the Special's profit is $10. Each model goes through two phases in the
production process, and there are only 100 hours available daily at the construction stage and
only 80 hours available at the finishing and inspection stage. Each Deluxe model requires 20
minutes of construction time and 10 minutes of finishing and inspection time. Each Special
model requires 15 minutes of construction time and 15 minutes of finishing and inspection time.
The company has also decided that the Special model must comprise at least 40 percent of the
production total.
(a) Formulate this as a linear programming problem.
(b) Find the solution that gives the maximum profit.
Answer:
(a) Let X1 = number of Deluxe models
X2 = number of Special models
Maximize
Subject to:
12X1 + 10X2
1/3 X1 + 1/4 X2 ≤ 100
1/6 X1 + 1/4 X2 ≤ 80
-0.4X1 + 0.6X2 ≥ 0
X1, X2 ≥ 0
(b) Optimal solution: X1 = 120, X2 = 240 Profit = $3,840
Diff: Difficult
Topic: FORMULATING LP PROBLEMS and GRAPHICAL SOLUTION TO AN LP
PROBLEM
LO: 7.2: Formulate a linear programming problem algebraically; LO 7.3: Graphically solve any
LP problem that has only two variables by both the corner point and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Application
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lOMoARcPSD|18541965
108) The Fido Dog Food Company wishes to introduce a new brand of dog biscuits (composed
of chicken and liver-flavored biscuits) that meets certain nutritional requirements. The liverflavored biscuits contain 1 unit of nutrient A and 2 units of nutrient B, while the chickenflavored ones contain 1 unit of nutrient A and 4 units of nutrient B. According to federal
requirements, there must be at least 40 units of nutrient A and 60 units of nutrient B in a package
of the new biscuit mix. In addition, the company has decided that there can be no more than 15
liver-flavored biscuits in a package. If it costs 1 cent to make a liver-flavored biscuit and 2 cents
to make a chicken-flavored one, what is the optimal product mix for a package of the biscuits in
order to minimize the firm's cost?
(a) Formulate this as a linear programming problem.
(b) Find the optimal solution for this problem graphically.
(c) Are any constraints redundant? If so, which one or ones?
(d) What is the total cost of a package of dog biscuits using the optimal mix?
Answer:
(a) Let X1 = number of liver-flavored biscuits in a package
X2 = number of chicken-flavored biscuits in a package
Minimize
Subject to:
X1 + 2X2
X1 + X2 ≥ 40
2X1 + 4X2 ≥ 60
X1 ≤ 15
X1, X2 ≥ 0
(b) Corner points (0,40) and (15,25)
Optimal solution is (15,25) with cost of 65.
(c) 2X1 + 4X2 ≥ 60 is redundant.
(d) minimum cost = 65 cents
Diff: Difficult
Topic: FORMULATING LP PROBLEMS and GRAPHICAL SOLUTION TO AN LP
PROBLEM
LO: 7.2: Formulate a linear programming problem algebraically; LO 7.3: Graphically solve any
LP problem that has only two variables by both the corner point and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Application
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lOMoARcPSD|18541965
109) Consider the following linear program:
Maximize
Subject to:
30X + 10Y
3X + Y ≤ 300
X + Y ≤ 200
X ≤ 100
Y ≥ 50
X,Y ≥ 0
(a) Solve the problem graphically. Is there more than one optimal solution? Explain.
(b) Are there any redundant constraints?
Answer:
(a) Corner points (0,50), (0,200), (50,50), (75,75), (50,150)
Optimum solutions: (75,75) and (50,150). Both yield a profit of $3,000.
(b) The constraint X1 ≤ 100 is redundant since 3X1 + X2 ≤ 300 also means that X1 cannot
exceed 100.
Diff: Difficult
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Application
110) Solve the following linear programming problem using the corner point method:
Maximize
Subject to:
10X + 1Y
4X + 3Y ≤ 36
2X + 4Y ≤ 40
Y≥3
X, Y ≥ 0
Answer: Feasible corner points (X,Y): (0,3) (0,10) (2.4,8.8) (6.75,3)
Maximum profit 70.5 at (6.75,3).
Diff: Difficult
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Application
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lOMoARcPSD|18541965
111) Solve the following linear programming problem using the corner point method:
Maximize
Subject to:
3X + 5Y
4X + 4Y ≤ 48
1X + 2Y ≤ 20
Y≥2
X, Y ≥ 0
Answer: Feasible corner points (X,Y): (0,2) (0,10) (4,8) (10,2)
Maximum profit is 52 at (4,8).
Diff: Difficult
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Application
112) Billy Penny is trying to determine how many units of two types of lawn mowers to produce
each day. One of these is the Standard model, while the other is the Deluxe model. The profit per
unit on the Standard model is $60, while the profit per unit on the Deluxe model is $40. The
Standard model requires 20 minutes of assembly time, while the Deluxe model requires 35
minutes of assembly time. The Standard model requires 10 minutes of inspection time, while the
Deluxe model requires 15 minutes of inspection time. The company must fill an order for 6
Deluxe models. There are 450 minutes of assembly time and 180 minutes of inspection time
available each day. How many units of each product should be manufactured to maximize
profits?
Let
X = number of Standard models to produce
Y = number of Deluxe models to produce
Maximize
Subject to:
60X + 40Y
20X + 35Y ≤ 450
10X + 15Y ≤ 180
Y≥6
X, Y ≥ 0
Answer: Maximum profit is $780 by producing 9 Standard and 6 Deluxe models.
Diff: Difficult
Topic: FORMULATING LP PROBLEMS and GRAPHICAL SOLUTION TO AN LP
PROBLEM
LO: 7.2: Formulate a linear programming problem algebraically; LO 7.3: Graphically solve any
LP problem that has only two variables by both the corner point and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Application
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lOMoARcPSD|18541965
113) Two advertising media are being considered for promotion of a product. Radio ads cost
$400 each, while newspaper ads cost $600 each. The total budget is $7,200 per week. The total
number of ads should be at least 15, with at least 2 of each type. Each newspaper ad reaches
6,000 people, while each radio ad reaches 2,000 people. The company wishes to reach as many
people as possible while meeting all the constraints stated. How many ads of each type should be
placed?
Answer: Let R = number of radio ads placed
N = number of newspaper ads placed
Maximize
Subject to:
2000R + 6000N
R + N ≥ 15
400R + 600N ≤ 7200
R≥2
N≥2
R, N ≥ 0
Feasible corner points (R,N): (9,6) (13,2) (15,2)
Maximum exposure 54,000 with 9 radio and 6 newspaper ads.
Diff: Difficult
Topic: FORMULATING LP PROBLEMS and GRAPHICAL SOLUTION TO AN LP
PROBLEM
LO: 7.2: Formulate a linear programming problem algebraically; LO 7.3: Graphically solve any
LP problem that has only two variables by both the corner point and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Application
114) Suppose a linear programming (minimization) problem has been solved and the optimal
value of the objective function is $300. Suppose an additional constraint is added to this
problem. Explain how this might affect each of the following:
(a) the feasible region.
(b) the optimal value of the objective function.
Answer:
(a) Adding a new constraint will reduce the size of the feasible region unless it is a redundant
constraint. It can never make the feasible region any larger. However, it could make the problem
infeasible.
(b) A new constraint can only reduce the size of the feasible region; therefore, the value of the
objective function will either increase or remain the same. If the original solution is still feasible,
it will remain the optimal solution.
Diff: Moderate
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM and FOUR SPECIAL CASES IN LP
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods; LO 7.6: Understand special issues in LP such as infeasibility,
unboundedness, redundancy, and alternative optimal solutions.
AACSB: Analytical thinking
Classification: Application
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lOMoARcPSD|18541965
115) Upon retirement, Mr. Klaws started to make two types of children's wooden toys in his
shop—Wuns and Toos. Wuns yield a variable profit of $9 each and Toos have a contribution
margin of $8 each. Even though his electric saw overheats, he can make 7 Wuns or 14 Toos each
day. Since he doesn't have equipment for drying the lacquer finish he puts on the toys, the drying
operation limits him to 16 Wuns or 8 Toos per day.
(a) Solve this problem using the corner point method.
(b) For what profit ratios would the optimum solution remain the optimum solution?
Answer: Let X1 = number of wuns/day
X2 = number of toos/day
Maximize
Subject to:
9X1 + 8X2
2X1 + 1X2 ≤ 14
1X1 + 2X2 ≤ 16
X1, X2 ≥ 0
(a) Corner points (0,0), (7,0), (0,8), (4,6)
(b) Optimum profit $84 at (4,6).
Diff: Difficult
Topic: FORMULATING LP PROBLEMS and GRAPHICAL SOLUTION TO AN LP
PROBLEM
LO: 7.2: Formulate a linear programming problem algebraically; LO 7.3: Graphically solve any
LP problem that has only two variables by both the corner point and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Application
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lOMoARcPSD|18541965
116) Susanna Nanna is the production manager for a furniture manufacturing company. The
company produces tables (X) and chairs (Y). Each table generates a profit of $80 and requires 3
hours of assembly time and 4 hours of finishing time. Each chair generates $50 of profit and
requires 3 hours of assembly time and 2 hours of finishing time. There are 360 hours of assembly
time and 240 hours of finishing time available each month. The following linear programming
problem represents this situation.
Maximize
80X + 50Y
Subject to:
3X + 3Y ≤ 360
4X + 2Y ≤ 240
X, Y ≥ 0
The optimal solution is X = 0, and Y = 120.
(a) What would the maximum possible profit be?
(b) How many hours of assembly time would be used to maximize profit?
(c) If a new constraint, 2X + 2Y ≤ 400, were added, what would happen to the maximum
possible profit?
Answer: (a) 6000, (b) 360, (c) It would not change.
Diff: Difficult
Topic: FORMULATING LP PROBLEMS and GRAPHICAL SOLUTION TO AN LP
PROBLEM
LO: 7.2: Formulate a linear programming problem algebraically; LO 7.3: Graphically solve any
LP problem that has only two variables by both the corner point and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Application
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lOMoARcPSD|18541965
117) As a supervisor of a production department, you must decide the daily production totals of a
certain product that has two models, the Deluxe and the Special. The profit on the Deluxe model
is $12 per unit, and the Special's profit is $10. Each model goes through two phases in the
production process, and there are only 100 hours available daily at the construction stage and
only 80 hours available at the finishing and inspection stage. Each Deluxe model requires 20
minutes of construction time and 10 minutes of finishing and inspection time. Each Special
model requires 15 minutes of construction time and 15 minutes of finishing and inspection time.
The company has also decided that the Special model must comprise at most 60 percent of the
production total.
Formulate this as a linear programming problem.
Answer: Let X1 = number of Deluxe models produced
X2 = number of Special models produced
Maximize
Subject to:
12X1 + 10X2
1/3X1 + 1/4X2 ≤ 100
1/6X1 + 1/4X2 ≤ 80
-1.5X1 + X2 ≤ 0
X1, X2 ≥ 0
Diff: Moderate
Topic: FORMULATING LP PROBLEMS
LO: 7.2: Formulate a linear programming problem algebraically.
AACSB: Analytical thinking
Classification: Application
118) Determine where the following two constraints intersect.
5X + 23Y ≤ 1000
10X + 26Y ≤ 1600
Answer: (108, 20)
Diff: Easy
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Application
119) Determine where the following two constraints intersect.
2X - 4Y = 800
−X + 6Y ≥ -200
Answer: (500, 50)
Diff: Easy
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Application
120) Two advertising media are being considered for promotion of a product. Radio ads cost
$400 each, while newspaper ads cost $600 each. The total budget is $7,200 per week. The total
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lOMoARcPSD|18541965
number of ads should be at least 15, with at least 2 of each type, and there should be no more
than 19 ads in total. The company does not want the number of newspaper ads to exceed the
number of radio ads by more than 25 percent. Each newspaper ad reaches 6,000 people, 50
percent of whom will respond; while each radio ad reaches 2,000 people, 20 percent of whom
will respond. The company wishes to reach as many respondents as possible while meeting all
the constraints stated. Develop the appropriate LP model for determining the number of ads of
each type that should be placed.
Answer: Let R = number of radio ads placed
N = number of newspaper ads placed
Maximize
or
0.20*2000R + 0.50*6000N
400R + 3000N
R + N ≥ 15
R + N ≤ 19
400R + 600N ≤ 7200
1.25R - N ≤ 7200
R≥2
N≥2
R, N ≥ 0
Diff: Moderate
Topic: FORMULATING LP PROBLEMS
LO: 7.2: Formulate a linear programming problem algebraically.
AACSB: Analytical thinking
Classification: Application
Subject to:
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lOMoARcPSD|18541965
121) Suppose a linear programming (maximization) problem has been solved and the optimal
value of the objective function is $300. Suppose a constraint is removed from this problem.
Explain how this might affect each of the following:
(a) the feasible region.
(b) the optimal value of the objective function.
Answer:
(a) Removing a constraint may, if the constraint is not redundant, increase the size of the feasible
region. It can never make the feasible region any smaller. If the constraint was active in the
solution, removing it will also result in a new optimal solution. However, removing an essential
constraint could cause the problem to become unbounded.
(b) Removal of a constraint can only increase or leave the same the size of the feasible region;
therefore, the value of the objective function will either increase or remain the same, assuming
the problem has not become unbounded.
Diff: Moderate
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM and FOUR SPECIAL CASES IN LP
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods; LO 7.6: Understand special issues in LP such as infeasibility,
unboundedness, redundancy, and alternative optimal solutions.
AACSB: Analytical thinking
Classification: Application
122) Consider the following constraints from a two-variable linear program.
1. X ≥ 0
2. Y ≥ 0
3. X + Y ≤ 50
If the optimal corner point lies at the intersection of constraints (2) and (3), what is the optimal
solution (X, Y)?
Answer: Y = 0, so X + 0 = 50, or X = 50. Thus the solution is (50, 0).
Diff: Easy
Topic: GRAPHICAL SOLUTION TO AN LP PROBLEM
LO: 7.3: Graphically solve any LP problem that has only two variables by both the corner point
and the isoprofit line methods.
AACSB: Analytical thinking
Classification: Application
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lOMoARcPSD|18541965
123) Consider a product mix problem, where the decision involves determining the optimal
production levels for products X and Y. A unit of X requires 4 hours of labor in department 1
and 6 hours of labor in department 2. A unit of Y requires 3 hours of labor in department 1 and 8
hours of labor in department 2. Currently, 1000 hours of labor time are available in department 1,
and 1200 hours of labor time are available in department 2. Furthermore, 400 additional hours of
cross-trained workers are available to assign to either department (or split between both). Each
unit of X sold returns a $50 profit, while each unit of Y sold returns a $60 profit. All units
produced can be sold. Formulate this problem as a linear program. (Hint: Consider introducing
other decision variables in addition to the production amounts for X and Y.)
Answer: Let X = the number of units of product X sold
Y = the number of units of product Y sold
C1= the number of cross-trained labor hours allocated to department 1
C2= the number of cross-trained labor hours allocated to department 2
Maximize:
50X + 60Y
Subject to:
4X + 3Y - C1 ≤ 1000
6X + 8Y - C2 ≤ 1200
C1 + C2 ≤ 400
X, Y ≥ 0
Diff: Difficult
Topic: FORMULATING LP PROBLEMS
LO: 7.2: Formulate a linear programming problem algebraically.
AACSB: Analytical thinking
Classification: Application
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lOMoARcPSD|18541965
124) A plastic parts supplier produces two types of plastic parts used for electronics. Type 1
requires 30 minutes of labor and 45 minutes of machine time. Type 2 requires 60 minutes of
machine hours and 75 minutes of labor. There are 600 hours available per week of labor and 800
machine hours available. The demand for custom molds and plastic parts are identical. Type 1
has a profit margin of $25 a unit and Type 2 has a profit margin of $45 a unit. The plastic parts
supplier must choose the quantity of Product A and Product B to produce which maximizes
profit.
(a) Formulate this as a linear programming problem.
(b) Find the solution that gives the maximum profit using either QM for Windows or Excel.
Answer:
(a)
Let
X1 = number of units of Product A produced
X2 = number of units of Product B produced
Maximize
Subject to:
25X1 + 45X2
0.50X1 + 1.25X2 ≤ 600
0.75X1 + X2 ≤ 800
X1, X2 ≥ 0
(b) X1 = 914.28, X2 = 114.28
Diff: Moderate
Topic: SOLVING FLAIR FURNITURE'S LP PROBLEM USING QM FOR WINDOWS AND
EXCEL 2016 AND EXCEL QM
LO: 7.2: Formulate a linear programming problem algebraically; LO 7.4: Use Excel
spreadsheets to solve LP problems.
AACSB: Analytical thinking
Classification: Application
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lOMoARcPSD|18541965
125) A company can decide how many additional labor hours to acquire for a given week.
Subcontractor workers will only work a maximum of 20 hours a week. The company must
produce at least 200 units of product A, 300 units of product B, and 400 units of product C. In 1
hour of work, worker 1 can produce 15 units of product A, 10 units of product B, and 30 units of
product C. Worker 2 can produce 5 units of product A, 20 units of product B, and 35 units of
product C. Worker 3 can produce 20 units of product A, 15 units of product B, and 25 units of
product C. Worker 1 demands a salary of $50/hr, worker 2 demands a salary of $40/hr, and
worker 3 demands a salary of $45/hr. The company must choose how many hours they should
contract with each worker to meet their production requirements and minimize labor cost.
(a) Formulate this as a linear programming problem.
(b) Find the optimal solution.
Answer:
(a)
Let
X1 = Worker 1 hours
X2 = Worker 2 hours
X3 = Worker 3 hours
Minimize
Subject to:
50X1 + 40X2 + 45X3
15X1 + 5X2 + 20X3 ≥ 200
10X1 + 20X2 + 15X3 ≥ 300
30X1 + 35X2 + 25X3 ≥ 400
X1, X2, X3 ≤ 20
X1, X2, X3 ≥ 0
(b) X1 = 0, X2 = 9.23, X3 = 7.69
Diff: Difficult
Topic: SOLVING FLAIR FURNITURE'S LP PROBLEM USING QM FOR WINDOWS AND
EXCEL 2016 AND EXCEL QM
LO: 7.2: Formulate a linear programming problem algebraically; LO 7.4: Use Excel
spreadsheets to solve LP problems.
AACSB: Analytical thinking
Classification: Application
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lOMoARcPSD|18541965
126) Consider the sensitivity report below:
(a) Which constraints are binding?
(b) Which constraints are non-binding?
(c) What is the increase in the objective value if 3 Corn are added?
Answer: (a) Corn and Sugar (b) Jugs and Hours (c) 15
Diff: Moderate
Topic: SENSITIVITY ANALYSIS
LO: 7.7: Understand the role of sensitivity analysis.
AACSB: Analytical thinking
Classification: Application
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127) Consider the sensitivity report below:
(a) Which constraints are binding?
(b) Which constraints are non-binding?
(c) What is the increase in the objective value if 3 Coffee are added?
Answer: (a) Floor and Budget (b) Coffee (c) 0
Diff: Moderate
Topic: SENSITIVITY ANALYSIS
LO: 7.7: Understand the role of sensitivity analysis.
AACSB: Analytical thinking
Classification: Application
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128) Consider the sensitivity report above.
(a) Which constraints are binding?
(b) What is the increase in the objective value if 30 Cabbage are added?
Answer: (a) Cabbage and Jars (b) 4.50
Diff: Moderate
Topic: SENSITIVITY ANALYSIS
LO: 7.7: Understand the role of sensitivity analysis.
AACSB: Analytical thinking
Classification: Application
129) Consider the sensitivity report above.
(a) If the current solution shows a maximum profit of $200, what is the profit if Chow Chow is
increased from $2.25 to $2.50?
(b) If the current solution shows a maximum profit of $200, what is the profit if Tomato is
decreased from $1.95 to $1.75?
Answer: (a) a $24 increase in profit to $224 (b) a $38.40 decrease in profit from $200 down to
$161.60
Diff: Moderate
Topic: SENSITIVITY ANALYSIS
LO: 7.7: Understand the role of sensitivity analysis.
AACSB: Analytical thinking
Classification: Application
130) Define dual price.
Answer: The dual price for a constraint is the improvement in the objective function value that
results from a one-unit increase in the right-hand side of the constraint.
Diff: Moderate
Topic: SENSITIVITY ANALYSIS
LO: 7.7: Understand the role of sensitivity analysis.
AACSB: Analytical thinking
Classification: Concept
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131) One basic assumption of linear programming is proportionality. Explain its need.
Answer: Rates of consumption exist and are constant. For example, if the production of 1 unit
requires 4 units of a resource, then if 10 units are produced, 40 units of the resource are required.
A change in the variable value results in a proportional change in the objective function value.
Diff: Moderate
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
LO: 7.1: Identify the basic assumptions and properties of linear programming (LP).
AACSB: Analytical thinking
Classification: Concept
132) List the 7 properties of linear programs.
Answer:
1. One objective function
2. One or more constraints
3. Alternative courses of action
4. Objective function and constraints are linear – proportionality and divisibility
5. Certainty
6. Divisibility
7. Nonnegative variables
Diff: Difficult
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
LO: 7.1: Identify the basic assumptions and properties of linear programming (LP).
AACSB: Analytical thinking
Classification: Concept
133) One basic assumption of linear programming is divisibility. Explain its need.
Answer: Solutions can have fractional values and need not be whole numbers. If fractional
values would not make sense, then integer programming would be required.
Diff: Moderate
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
LO: 7.1: Identify the basic assumptions and properties of linear programming (LP).
AACSB: Analytical thinking
Classification: Concept
134) Define infeasibility with respect to an LP solution.
Answer: This occurs when there is no solution that can satisfy all constraints simultaneously.
Diff: Moderate
Topic: FOUR SPECIAL CASES IN LP
LO: 7.6: Understand special issues in LP such as infeasibility, unboundedness, redundancy, and
alternative optimal solutions.
AACSB: Analytical thinking
Classification: Concept
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135) Define unboundedness with respect to an LP solution.
Answer: This occurs when a linear program has no finite solution. The result implies that the
formulation is missing one or more crucial constraints.
Diff: Moderate
Topic: FOUR SPECIAL CASES IN LP
LO: 7.6: Understand special issues in LP such as infeasibility, unboundedness, redundancy, and
alternative optimal solutions.
AACSB: Analytical thinking
Classification: Concept
136) Define alternate optimal solutions with respect to an LP solution.
Answer: More than one optimal solution point exists because the objective function is parallel to
a binding constraint.
Diff: Moderate
Topic: FOUR SPECIAL CASES IN LP
LO: 7.6: Understand special issues in LP such as infeasibility, unboundedness, redundancy, and
alternative optimal solutions.
AACSB: Analytical thinking
Classification: Concept
137) How does the case of alternate optimal solutions, as a special case in linear programming,
compare to the two other special cases of infeasibility and unboundedness?
Answer: With multiple alternate solutions, any of those answers is correct. In the other two
cases, no single answer can be generated. Alternate solutions can occur when a problem is
correctly formulated whereas the other two cases most likely have an incorrect formulation.
Diff: Moderate
Topic: FOUR SPECIAL CASES IN LP
LO: 7.6: Understand special issues in LP such as infeasibility, unboundedness, redundancy, and
alternative optimal solutions.
AACSB: Analytical thinking
Classification: Concept
138) Compare the shadow price to the dual price.
Answer: For maximization problems, the shadow and dual prices are equal, but for minimization
problems, the shadow price will be the negative of the dual price.
Diff: Moderate
Topic: SENSITIVITY ANALYSIS
LO: 7.7: Understand the role of sensitivity analysis.
AACSB: Analytical thinking
Classification: Concept
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139) One basic assumption of linear programming is certainty. What does this imply and how
reasonable is this assumption?
Answer: The exact values of numbers in the objective function and constraints are known and
do not change. Answers may vary as to how reasonable it is. For a classic product mix problem
you are expressing confidence in your knowledge of the bill of materials and inventory levels
entering the planning period as well as costs and selling prices.
Diff: Moderate
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
LO: 7.1: Identify the basic assumptions and properties of linear programming (LP).
AACSB: Analytical thinking
Classification: Concept
140) One basic assumption of linear programming is non-negativity. What does this imply and
how reasonable is this assumption?
Answer: This assumption states that only positive values for decision variables make sense.
From a practical standpoint, if negative values were permissible, it would permit finished goods
to be disassembled or deconstructed in some way as to provide more resources to make finished
goods of a different kind.
Diff: Moderate
Topic: REQUIREMENTS OF A LINEAR PROGRAMMING PROBLEM
LO: 7.1: Identify the basic assumptions and properties of linear programming (LP).
AACSB: Analytical thinking
Classification: Concept
141) What is George Dantzig's contribution to linear programming?
Answer: George Dantzig was an Air Force mathematician assigned to work on logistics
problems. He saw that many problems involving limited resources and more than one demand
could be set up in terms of a series of equations and inequalities, and he subsequently developed
the simplex algorithm for solving these problems. Although early applications of linear
programming were military in nature, industrial applications rapidly became apparent with the
widespread use of business computers. The simplex algorithm developed by Dantzig is still the
basis for much of the software used for solving linear programs today.
Diff: Moderate
Topic: FORMULATING LP PROBLEMS
LO: 7.2: Formulate a linear programming problem algebraically.
AACSB: Analytical thinking
Classification: Concept
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