Digital Controls, Inc. (DCI) manufacturers 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 assembly time. For next week the Newark plant has 600 minutes of injection-molding time available and 1080 minutes of assembly available. The manufacturing cost is $ 10 per case for model A and $6 per case of 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 to fill customers’ 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 plant 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 10 AM+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 sensitivity report is shown in the following figure:
- What is the optimal solution and what is the optimal value of the objective function?
- Which constraints are binding?
- What are the shadow prices? Interpret each.
If you could change the right-hand-side of one constraint by one unit, which one would you choose? Why
