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Part I: An automobile manufacturer has four outdated plants in Michigan, Ohio, California and New York.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.