CASE #10 – Spring 2023
Part I: An automobile manufacturer has four outdated plants in Michigan, Ohio, California and New York. Management is considering modernizing these plants to manufacture Engine Blocks and Transmissions for a new model of car. The cost of modernizing each plant and the manufacturing capacities, before and after modernization, are as follows:
Cost of
Production Capacities
Modernization
Before Modernization
After Modernization
PLANT
(millions)
Eng.Blocks
Transmissions
Eng.Blocks
Transmisions
Michigan
25
200,000
150,000
500,000
300,000
Ohio
35
500,000
200,000
800,000
400,000
California
35
150,000
300,000
400,000
800,000
New York
40
400,000
300,000
900,000
600,000
The projected needs are 1,700,000 Engine Blocks and 1,600,000 Transmissions. Management wants to decide which plants to modernize to meet projected manufacturing needs and at the same time, minimize the total cost of modernization.
(a) Develop a linear program to solve this problem. Write the model here.
(b) Solve the problem in Excel and write a short report with your answer.
(c) Add one or more constraints that say that Michigan and California cannot be modernized together. Report the new solution and overall cost.
(d) To the original model, that is, drop the constraint in (c), add one or more constraints that ensure that if New York is modernized, then Ohio is as well. Report the new solution and overall cost.
(e) To the original model add one or more constraints to ensure that no more than 2 plants will be modernized. Report the new solution and overall cost.
Part II: Suppose now that the productions costs are different in the four plants and the company would like to minimize the total production plus modernization costs. The productions costs per unit are as follows:
PLANT
Engine
Blocks
Transmissions
Michigan
2600
800
Ohio
2500
600
California
2200
650
New York
2200
550
(f) Develop a linear program to solve this problem. Write the model here.
(g) Solve the problem in Excel and write a short report with your answer.