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?

Blue computers, a major pc manufacturer in the united states, currently has plants in kentucky and pennsylvania. the kentucky plant has a capacity of 1 million units a year and the pennsylvania plant has a capacity of 1.5 million units a year. the firm divides the united states into five markets: northeast, southeast, midwest, south, and west. each pc sells for $1,000. the firm anticipates a 50 perc~nt growth in demand (in each region) this year (after which demand will stabilize) and wants to build a plant with a capacity of 1.5 million units per year to accommodate the growth. potential sites being considered are in north carolina and california. currently the firm pays federal, state, and local taxes on the income from each plant. federal taxes are 20 percent of income, and all state and local taxes are 7 percent of income in each state. north carolina has offered to reduce taxes for the next 10 years from 7 percent to 2 percent. blue computers would like to take the tax break into consideration when planning its network. consider income over the next 10 years in your analysis. assume that all costs remain unchanged over the 10 years. use a discount factor of 0.1 for your analysis. annual fixed costs, production and shipping costs per unit, and current regional demand (before the 50 percent growth) are shown in table 5-13. (a) if blue computers sets an objective of minimizing total fixed and variable costs, where should they build the new plant? how should the network be structured? (b) if blue computers sets an objective of maximizing after-tax profits, where should they build the new plant? how should the network be structured? variable production and shipping cost ($/unit) annual fixed cost northeast southeast midwest south west (million$) kentucky 185 180 175 175 200 150 pennsylvania 170 190 180 200 220 200 n. carolina 180 180 185 185 215 150 california 220 220 195 195 175 150 demand ('000 units/month) 700 400 400 300 600