Chapter 5 Exam
Name:
MAT115
Directions: Show all work. Identify the solution region on all graphs.
1) Graph the following inequality on the grid provided below. (4 points)
-3x - 4y > 8
2) Solve the System of inequalities by graphing. (8 points)
5x + 2y < 10
2x – 5y > 10
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3) At the concert t-shirts sell for $30 and hats sell for $22. How many of each of these must be sold to
produce sales of at least $5000?
Answer only the following questions. Do NOT solve the problem.
a) Define the decision variables. (2 points)
b) Write an inequality AND the non-negative constraints that describe this situation (5 points)
4) A Starbucks Frappuccino costs $ 4.50 each and the biscotti costs $ 2.25 each. How many of each
can you purchase if you can spend no more than $ 18.00?
a) Define the decision variables. (2 points)
b) Write an inequality and the non-negative constraints that describe this situation. (5 points)
c) Show the solution set for the problem on the graph above. (5 points)
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5) A steel company produces two parts, Part A and Part B. Part A requires 6 hours casting time
and 4 hours firing time. Part B requires 8 hours casting time and 3 hours firing time. The
maximum amount of time available for cast is 85 hours. The maximum amount of time
available for firing is 70 hours.
The company makes a profit of $2.00 on Part A and a profit of $ 6.00 on Part B. How many of
each part should the company produce to maximize profit?
Answer only the following questions. Do NOT solve the problem.
a) Define the decision variables. (2 points)
b) What are the constraints and the non-negative constraints? (10 points)
c) What is the objective function?
(5 points)
6) Determine the corner points of this solution region. (7 points)
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7) The corner points for the bounded feasible region have been determined for the following system
of linear inequalities:
x + 2y  8
3x + 2 y  9
x, y  0
Those corner points are pt A = (0, 0), pt B = (0, 4), pt C (2, 3) and pt D = (3, 0).
a) Find the optimal solution that maximizes the objective function P = 2x +4y.
(7 points)
b) What is the maximum value of P at that point? (1 point)
8) Solve the following linear programming problem geometrically by determining the feasible region
and testing the resulting corner points (15 points). Make sure to show the corner point table.
Minimize:
Subject to:
C = 90x + 182y
6x + 3y < 24
3x + 6y > 30
x > 0 and y > 0
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9) Lake Norman Sail manufactures regular and competition sails. Each regular sail takes 2
hours to cut and 4 hours to sew. Each competition sail takes 3 hours to cut and 10 hours to
sew. There are 150 hours available in the cutting department and 380 hours available in the
sewing department. (22 points)
The company makes $100 profit on each regular sail and $200 on each competition sail. How
many of each type should the company produce to maximize their profit?
a) Define the Decision Variables.
b) Write the problem constraints based on the given information.
c) Write the non-negative constraints.
d) Write the Objective Function.
e) Graph the Feasible Region.
f) Construct a Corner Point
table.
g) Which corner point yields
the optimal solution?
h) Write a complete sentence that interprets and explains the solution to the original problem.
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