Digital Controls, Inc. (DCI), manufactures two models of a radar gun used by police to monitor the speed of automobiles. Model A has an accuracy of plus or minus 1 mile per hour, whereas the smaller model B has an accuracy of plus or minus 3 miles 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 Newark, New Jersey. Each model A case requires 4 minutes of injection-molding time and 6 minutes of assembly time. Each model B case requires 3 minutes of injection-molding time and 8 minutes of assembly time. For next week, the Newark plant has 600 minutes of injection-molding time available and 1080 minutes of assembly time available. The manufacturing cost is $10 per case for model A and $6 per case for model B. Depending upon demand and the time available at the Newark 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 $14 for each model A case and $9 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 Newark 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 = number of cases of model A manufactured
BM = number of cases of model B manufactured
AP = number of cases of model A purchased
BP = number of cases of model B purchased
The linear programming model that can be used to solve this problem is as follows:
Min 10AM + 6BM + 14AP + 9BP
s.t
1AM + + 1AP + = 100 Demand for model A
1BM + 1BP = 150 Demand for model B
4AM + 3BM ‰¤ 600 Injection molding time
6AM + 8BM ‰¤ 1080 Assembly time
AM, BM, AP, BP ‰¥ 0
The computer solution is shown in Figure 3.18.
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 values? Interpret each.
d. If you could change the right-hand side of one constraint by one unit, which one would you choose? Why?
Figure 3.18

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Optimal Objective Value - 2170.00000 Variable Value Reduced Cost AB BM AP BD 100.00000 60.00000 0.00000 90.00000 0.00000 0.00000 1.75000 0.00000 Constraint Slack/Surplus Dual Value 0.00000 0.00000 20.00000 0.00000 12.25000 9.00000 0.00000 0.37500 Objective Allowable Increase Allowable Variable Coefficient Decrease 10.00000 6.00000 14.00000 9.00000 1.75000 3.00000 Infinite 2.33333 AB BM Infinite 2.33333 1.75000 3.00000 BD Allowable Allowable Constraint Value Increase Decrease 100.00000 150.00000 600.00000 1080.00000 11.42857 Infinite Infinite 53.33333 100.00000 90.00000 20.00000 480.00000