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130 CHAPTER 3 LINEAR PROGRAMMING: SENSITIVITY ANALYSIS AND INTERPRETATION OF SOLUTION

c. Identify the range of feasibility for the right-hand side values.
d. If the number of fan motors available for production is increased by 100, will the dual
price for that constraint change? Explain.
15 Digital Controls, Inc. (DCI), manufactures two models of a radar speed device used by
police to monitor the speed of automobiles. Model A has an accuracy of plus or minus
one km per hour, whereas the smaller model B has an accuracy of plus or minus three km
per hour. For the next week, the company has orders for 100 units of model A and 150
units of model B. Although DCI purchases all the electronic components used in both
models, the plastic cases for both models are manufactured at a DCI plant in China.
Each model A case requires four minutes of injection-moulding time and six minutes of
assembly time. Each model B case requires three minutes of injection-moulding time
and eight minutes of assembly time. For next week, the plant has 600 minutes of
injection-moulding time available and 1080 minutes of assembly time available. The
manufacturing cost is E10 per case for model A and E6 per case for model B.
Depending upon demand and the time available at the plant, DCI occasionally
purchases cases for one or both models from an outside supplier in order to fill
customer orders that could not be filled otherwise. The purchase cost is E14 for each
model A case and E9 for each model B case. Management wants to develop a
minimum-cost plan that will determine how many cases of each model should be
produced at the plant and how many cases of each model should be purchased. The
following decision variables were used to formulate a linear programming model for this
problem:
AM ¼ number of cases of model A manufactured

BM ¼ number of cases of model B manufactured
AP ¼ number of cases of model A purchased
BP ¼ number of cases of model B purchased

The linear programming model that can be used to solve this problem is as follows:

Min 10AM þ 6BM þ 14AP þ 9BP
s:t
1AM þ 1AP ¼ 100 Demand for model A
1BM þ IBP ¼ 150 Demand for model B
4AM þ 3BM 600 Injection-moldingtime
6AM þ 8BM 1080 Assembly time
AM; BM; AP; BP 0

The computer solution developed is shown in Figure 3.19.
a. What is the optimal solution, and what is the optimal value of the objective function?
b. Which constraints are binding?
c. What are the dual prices? Interpret each.
d. If you could change the right-hand side of one constraint by one unit, which one would
you choose? Why?
16 Refer to the computer solution of Problem 15 in Figure 3.19.
a. Interpret the ranges of optimality for the objective function coefficients.
b. Suppose that the manufacturing cost increases to E11.20 per case for model A. What is
the new optimal solution?

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