1. An automobile manufacturer has five outdated plants: one each in Michigan, Ohio, and California and two in New York. Management is considering modernizing these plants to manufacture engine blocks and transmissions for a new model car. The costs to modernize each plant and the manufacturing capacity after modernization are as follows:
|
Plant
|
Cost [$ millions]
|
Engine Blocks [1000s]
|
Transmissions [1000s]
|
|
Michigan
|
25
|
500
|
300
|
|
New York
|
35
|
800
|
400
|
|
New York
|
35
|
400
|
800
|
|
Ohio
|
40
|
900
|
600
|
|
California
|
20
|
200
|
300
|
The projected needs are for total capacities of 900,000 engine blocks and 900,000 transmissions. Management wants to determine which plants to modernize to meet projected manufacturing needs and, at the same time, minimize the total cost of modernization.
Formulate a binary (0-1 integer) programming model that could be used to determine the optimal solution to the modernization question facing management.
Solve the model formulated in part a) and provide a recommendation for management.