Digital Controls manufactures two types of radar gun. Model A has accuracy of 1 mile per hour, whereas Model B has accuracy of 3 miles per hour. For the next week there are orders for 100 of Model A and 150 of Model B. Each model A case requires 4 minutes of injection modeling time and 6 minutes of assembly time. Each Model B requires 3 minutes of injection time and 8 minutes of assembly time. For the next week, the plant has 600 minutes of injection time and 1080 minutes of assembly time. The manufacturing costs are $10 per case for Model A and $6 per case for Model B. Sometimes, the plant needs to purchase parts from an outside source, at a cost of $14 for Model A and $9 for Model B. The following decision variables should be used. 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
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?