DSCI 3870.001: Management Science
Exam # 1
Version: Blue
October 2, 2012
Time allotted: 75 minutes
Name:
SID#:
Please read this carefully
The questions, which you attempt today, consist of True/False and multiple-choice
questions worth 133 points total. Some of these questions are based on descriptive
cases. There are a total of 30 questions.
Please answer all the questions on the scantron sheet provided. After you are done,
please turn in the scantron and this question booklet.
Please note that you have to enter your name and Student ID Number (SID#) in the
above area and on the scantron. Failure to do so will result in a grade of zero .
This is an open book exam. You are allowed to use a programmable calculator and/or laptop
computer. Besides the textbook, you are allowed to use only those notes, which have been
handed out in class, and notes, which you have recorded during, class sessions. Be sure to
allocate you time wisely between the multiple choice and T/F questions.
Acronyms such as LP, LHS (left-hand side), RHS (right-hand side) etc. may have been
used. If you are unsure about an acronym, please ask me/the invigilator immediately.
Best of luck!!
1. An airplane designer tests a model airplane in a wind tunnel to learn about the potential
flying characteristics of the full-size airplane. We call this kind of model
a. An iconic model
b. An analog model
c. A mathematical model
d. A qualitative model
2. Corporate income tax rate is a controllable input in many decision models.
a. True
b. False
3. There is exactly one solution that provides the optimal value for the objective function in
the case of alternative optimal solutions.
a. True
b. False
4. The technique that permits the inclusion of subjective factors in arriving at a
recommendation decision is:
a. Decision analysis
b. Goal programming
c. Analytical hierarchy process
d. Forecasting
e. Simulation
5.
a.
b.
c.
d.
Which of the following statements is NOT true?
A feasible solution satisfies all constraints.
An optimal solution satisfies all constraints.
An infeasible solution violates all constraints.
A feasible solution point does not have to lie on the boundary of the feasible region.
6. In the dialog box shown below the Cell Reference and Constraint input fields usually refer to
a.
b.
c.
d.
e.
the Max and Min objective function of the model respectively
the LHS and RHS respectively of one or more variables
the LHS and RHS respectively of only a single variable
the LHS and RHS respectively of one or more constraints
the LHS and RHS respectively of only a single constraint
1
7.
a.
b.
c.
d.
Decision alternatives
should be identified before decision criteria are established.
are limited to quantitative solutions
are evaluated as a part of the problem definition stage.
are best generated by brain-storming.
The following six questions relate to the GRAPHICAL LP PROBLEM given below:
Examine the LP formulation shown below. For your convenience I have already graphed the axes,
although I have not labeled the constraints nor identified the feasible region. Please see Figure 1.
You will also have to construct and move the iso-lines (objective function) in order to find the
optimal solution.
A
I
II
III
B
C
V
IV
Figure 1: Coordinate Axes and Constraints for LP Problem
Objective Function:
S.t.
5X+6Y
3 X + Y > 15
X + 2Y ≤ 12
3 X + 2Y ≤ 24
X, Y > 0
2
8. What is the Constraint labeled A shown in Figure -1?
a. 5X + 6Y
b. 3X + Y > 15
c. X + 2Y ≤ 12
d. X,Y ≥ 0
e. 3X + 2Y < 24
9. What is the Constraint labeled B shown in Figure -1?
a. 5X + 6Y
b. 3X + Y > 15
c. X + 2Y ≤ 12
d. X,Y ≥ 0
e. 3X + 2Y < 24
10. What is the Constraint labeled C shown in Figure -1?
a. 5X + 6Y
b. 3X + Y > 15
c. X + 2Y ≤ 12
d. X,Y ≥ 0
e. 3X + 2Y < 24
11. What is the feasible region shown in Figure-1?
a. Ⅰ
b. Ⅱ
c. Ⅲ
d. Ⅳ
e. Ⅴ
12. What is the optimal objective function value if one were to Maximize the objective function?
a. 48
b. 25
c. 43.2
d. 40
e. 0
13. What is the optimal solution if one were to Minimize the objective function?
a. 48
b. 40
c. (5,0)
d. 0
e. (8,0)
3
The next three questions are based on the following case:
The relationship d= 8500� 60p describes what happens to demand (d) as price (p) varies. Here,
price can vary between $20 and $150.
14.
How many units can be sold at the $20 price and at the $70 price respectively?
a.
7300, 4300
b.
4300, 7300
c.
6000, 4300
d.
7300, 4000
15. The expression for total revenue is given as
a.
p – (8500� 60p)
b.
p (8500� 60p)
c.
d (8500� 60p)
d.
d/(8500� 60p)
16. Consider prices of $70, $80, and $140. Among these, which price alternative will
maximize total revenue?
a.
$70
b.
$80
c.
$140
d.
All of the above
The next two questions are based on the following case
As part of their application for a loan to buy Lakeside Farm, a property they hope to develop as a
bed-and-breakfast operation, the prospective owners have projected (assume 30 days per month).
Monthly fixed cost (loan payment, taxes, insurance, maintenance)
$ 6000
Variable cost per occupied room per night
$ 20
Revenue per room per night
$ 75
Let x be the number of rooms (Demand usually exceeds 10 rooms per night)
17. The expression for total profit is given as,
a. 75x – (6000 + 20x)
b. 6000+ 600x
c. 1650x – 6000
d. 75x
4
18. How many rooms are needed in order to breakeven?
a. 3
b. 4
c. 5
d. 6
19. Which of the following mathematical relationship would be acceptable in a linear programming
model?
a. X1 + X2 = 2
b. 3X12 - 2X2 ≥ 10
c. X1X2 – X3 ≤ 1
d. 2X1 + 3X2 ≠ 20
e. Both a and d are acceptable.
20. The constraint 0.5 X1 + 0.5 X2 ≤ 15 passes through the point (10, 20)
a. True
b. False
21. Consider a linear program (LP):
Max 10X + 20Y
st. X ≥ 1
0.5 X – Y ≥ � 2
X,Y ≥ 0
a.
b.
c.
d.
The feasible region for this LP does not exist
The feasible region for this LP is a bounded region
The feasible region for this LP is an unbounded region
The feasible region for this LP is a line segment
The next three questions are based on the following case:
A manufacturer of coffee machines makes two kinds of products: LS and TA. Each LS requires 8
hours of labor and each TA requires 6 hours of labor. Each LS needs 20 ounces of alumina and
whereas each TA needs 30 ounces of alumina. The manufacturer expects to have 1000 labor hours
and 300 ounces of alumina available. Three LS require 2 plastic plates whereas each TA requires 3
plastic plates. The manufacturer has 200 plastic plates at her disposal. She expects to make a profit
of $30 on each type of LS that she sells and $50 on each TA.
Let X = the number of LS manufactured and Y= the number of TA manufactured.
5
22.
The Objective function for the problem is:
a. Max 30X + 50Y
b. Max 20X+ 30Y
c. Min 20X+ 30Y
d. Max 30X +20Y
e. Min 30X + 50Y
23.
Which of the following constraint represents the restriction on plastic plates?
a. 2X + 9Y ≥ 600
b. 2X + 3Y < 200
c. 2X + 3Y ≥ 200
d. 2X + 9Y < 600
e. 2X + 3Y = 200
24. If one were to include an additional constraint of the type X – Y > 0, then it would mean that:
a. We can manufacture one or the other type of coffee machines but not both.
b. If we make any LS then we have to make at least that many TA
c. If we make any TA then we have to make at least that many LS
d. We have to make the exact same number of both types of coffee machines.
e. We cannot make “negative” number of LS
6
40
Payoff: 1.0 D1 + 1.0 D2 = 133.3
36
32
TimeBlnc1: -1.0 D1 + 4.0 D2 = 30.0
28
Line1: 3.0 D1 + 6.0 D2 = 480.0
24
Line2: 4.0 D1 + 2.0 D2 = 480.0
20
16
12
8
PrdtBlnc: 1.0 D1 - 1.0 D2 = 0.0
TimeBlnc2: 1.0 D1 - 4.0 D2 = 30.0
4
0
0
6
12
18
24
30
36
42
48
54
60
66
72
78
84
90
96
102 108 114 120
D1
Line1: 3.0D1 + 6.0D2 <= 480.0
Line2: 4.0D1 + 2.0D2 <= 480.0
PrdtBlnc: 1.0D1 - 1.0D2 >= 0.0
TimeBlnc1: -1.0D1 + 4.0D2 <= 30.0
TimeBlnc2: 1.0D1 - 4.0D2 <= 30.0
25.
Consider the optimal solution (displayed in the graphic above/on previous page) to one of
the variants discussed in the “Workload Balancing” case that was solved in class. If we were
to add the constraint:
D1 + 2 D2 ≥ 72, to the model displayed in the graphic, we would expect
a. the optimal solution to stay the same.
b. the optimal solution to change.
c. the model to become infeasible.
d. the model to become unbounded.
e. alternate optimal solutions.
7
The next three questions are based on the following case:
Maxwell Manufacturing makes two models of felt tip marking pens. Requirements for each lot of
pens are given below. The availability of plastic is 36, ink assembly is 40, and molding time is 30.
The profit for Fliptop model is $100 per lot, Tiptop model is $150 per lot. The number of lots of
Fliptop pens produced should not be less than 75% of both type of pens produced.
Let F = the number of lots of Fliptop pens to produce
Let T = the number of lots of Tiptop pens to produce
Plastic
Ink Assembly
Molding Time
Fliptop Model
3
5
5
Tiptop Model
4
4
2
26.
a.
b.
c.
d.
e.
What is the constraint for Molding Time?
3F + 4T = 30
5F + 2T < 30
5F + 2T < 40
5F + 2T > 30
5F + 4T > 30
27.
a.
b.
c.
d.
e
What is the objective function?
Max. 3F + 4T
Min. 100F + 150T
Min. 5F + 2T
Min. 5F + 4T
Max. 100F + 150T
28.
a.
b.
c.
d.
e
What is the constraint on the number of lots of Fliptop pens?
0.75F – T ≤ 0
F – 0.75T ≤ 0
F− 3T ≥ 0
F + T ≥ 0.75
F – T = 0.75
8
The next two questions are based on the following case and on MS Excel outputs that follow
Baba Budan, the manager of Babushka Bakery prepares a spread sheet model to keep track of his
weekly profit. After developing a basic model he is interested in knowing how the changes in cake
price affect his revenue, processing cost and profit. His objective is profit maximization. For this he
uses Excel’s data table command to perform sensitivity analysis. The prices he is considering are in
$0.20 intervals. Answer the questions based on the sensitivity analysis shown in the MS Excel
output that follows. In the output, ”($000's)” means in thousands of dollars and “(000's)” means in
thousands of units.
29. What is the row input cell in this data table?
a. C26
b. C10
c. C5
d. This is a Data Table 1. There is no row input cell.
e. This is a Data Table 2. There is no row input cell.
30.
Assuming that Baba Budan has the power to set the optimal cake price, what would be
(approximately) the maximum profit before tax?
a.
b.
c.
d.
e.
$18,000
$19,000
$ 7.80
$ 20,000
$ 19.50
MS Excel output follows
9
B
2
C
Babushka Bakery--Weekly Profit
Model
3
4
Decision Variables
5
Cake Price
$7.00
6
7
Parameters
8
Unit cost, fruit Filling ($ Per cake)
$2.50
9
Unit cost, Dough ($ per cake)
$0.40
10
Fixed cost ($000's)
11
Equation coefficients
12
Cake demand Equation
13
Intercept
32
14
Slope (Linear Coefficient)
-3
15
Processing cost Equation
16
Linear coefficient
0.8541
17
Quadratic coefficient
0.0621
18
Physical results (000's)
19
Cakes demanded and sold
20
Financial Results ($000's)
21
Revenue
$ 77
22
Processing cost
$ 17
23
Ingredients cost
$ 32
24
Overhead cost
$ 10
25
Total cost
$ 59
26
Profit (Before tax)
$ 18
$10
11
10
Data Table:
$ 6.00
$
6.20
$ 6.40
$ 6.80
$ 7.00
$
7.20
$
7.40
$ 7.60
$
7.80
$
8.00
$
8.20
Revenue
$ 77.00
$ 84.00
$ 83.08
$ 81.92
$ 78.88
$77.00
$ 74.88
$ 72.52
$69.92
$ 67.08
$ 64.00
$ 60.68
Total Cost
$ 58.81
$ 74.73
$ 71.46
$ 68.23
$ 61.90
$58.81
$ 55.76
$ 52.75
$49.79
$ 46.88
$ 44.01
$ 41.18
Profit (Before tax)
$ 18.19
$ 9.27
$ 11.62
$ 13.69
$ 16.98
$18.19
$ 19.12
$ 19.77
$20.13
$ 20.20
$ 19.99
$ 19.50
11