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Revised January 2011
Chapter 03 Assignments:
Problem 1
Consider the following linear program:
Min
8X + 12Y
s.t.
1
X +
3Y
≥
9
2X + 2Y
≥
10
6X + 2Y
18
X, Y
≥
0
a. Use the graphical solution procedure to find the optimal solution.
b. Assume that the objective function coefficient for X
changes from 8 to 6. Does
the optimal solution change? Use the graphical solution procedure to find the
new optimal solution.
c. Assume that the objective function coefficient for X remains 8, but the objective func
tion coefficient for Y changes from 12 to 6. Does the optimal solution change? Use
the graphical solution procedure to find the new optimal solution.
d. The Management Scientist computer solution for the linear program in part (a)
provides the following objective coefficient range information:
Variable
Lower Limit
Current Value
Upper Limit
X
4
8
12
Y
8
12
24
How would this objective coefficient range information help you answer parts (b) and(c)
prior to resolving the problem?
Problem 2
Refer to the Kelson Sporting Equipment, Inc., make two different types of baseball
gloves: a regular model and a catcher’s model. The firm has 900 hours of production
time available in its cutting and sewing department, 300 hours available in its finishing
department, and 100 hours available in its packing and shipping department. The
production time requirements and the profit contribution per glove are given in the
following table.
Production Time (hours)
Model
Cutting and
Sewing
Finishing
Packing &
Shipping
Profit per
Glove
Regular
1
1/2
1/8
$5
Catcher’s
3/2
1/3
1/4
$8
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View Full DocumentLetting
R= number of regular gloves to produce
C= number of catcher’s gloves to produce
leads to the following formulation:
Max
5 R + 8 C
s.t.
R + 3/2 C
900
Cutting and sewing
1/2 R + 1/3 C
300
Finishing
1/8 R + 1/4 C
100
Packaging and shipping
R, C ≥
0
The computer solution obtained using The Management Scientist is shown in the
following table.
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 Spring '11
 abc

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