Chapter 5: Homework 1. An automobile manufacturer has five outdated plants: one
ID: 1720405 • Letter: C
Question
Chapter 5: Homework
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 An automobile manufacturer has five outdated plants: one each in Michigan, Ohio, and California and two in New York.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 cost 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.
a) Solve and formulate the binary programming model that could be used to determine the optimal solution to the modernization question facing management and provide a recommendation for management
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
Explanation / Answer
Let:
1 denote the Michigan plant
2 denote the first New York plant
3 denote the second New York plant
4 denote the Ohio plant
5 denote the California plant
It is not possible to meet needs by modernizing only one plant.
So, we draw the following table which shows the options which involve modernizing two plants.
1 2 3 4 5 Transmission Capacity Engine Block Capacity Feasible (Y/N) Cost 700 1300 N 1100 900 Y 60 900 1400 Y 65 600 700 N 1200 1200 Y 70 1000 1700 Y 75 700 1000 N 1400 1300 Y 75 1100 600 N 900 1100 Y 60Related Questions
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