The shipping cost per unit from each plant to each distribution center is as follows: Plant Site Detroit Toledo Denver Kansas City St. Louis Boston 5 4 9 10 8 Distribution Centers Atlanta 2 3 7 4 4 Houston 3 4 5 2 3 (a) Develop a mixed-integer programming model that could be used to help Martin-Beck determine which new plant or plants to open in order to satisfy anticipated demand. Solve the model and answer the following questions. What is the optimal cost? $ 104800 What is the optimal set of plants to open? Detroit & Toledo

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The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional distribution
centers located in Boston, Atlanta, and Houston. Because of an anticipated increase in demand, Martin-Beck plans to increase capacity by
constructing a new plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas City. The estimated annual fixed cost and the
annual capacity for the four proposed plants are as follows:
Proposed Plant
Detroit
Toledo
Denver
Kansas City
The company's long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows:
Distribution Center
Boston
Atlanta
Annual Fixed Cost
$175,000
$300,000
$375,000
$500,000
Houston
Annual Capacity
20,000
30,000
40,000
10,000
Annual Demand
30,000
20,000
20,000
Transcribed Image Text:The Martin-Beck Company operates a plant in St. Louis with an annual capacity of 30,000 units. Product is shipped to regional distribution centers located in Boston, Atlanta, and Houston. Because of an anticipated increase in demand, Martin-Beck plans to increase capacity by constructing a new plant in one or more of the following cities: Detroit, Toledo, Denver, or Kansas City. The estimated annual fixed cost and the annual capacity for the four proposed plants are as follows: Proposed Plant Detroit Toledo Denver Kansas City The company's long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows: Distribution Center Boston Atlanta Annual Fixed Cost $175,000 $300,000 $375,000 $500,000 Houston Annual Capacity 20,000 30,000 40,000 10,000 Annual Demand 30,000 20,000 20,000
The shipping cost per unit from each plant to each distribution center is as follows:
Plant Site
Detroit
Toledo
Denver
Kansas City
St. Louis
Boston
5
4
9
10
8
Distribution Centers
Atlanta
2
3
7
4
4
Houston
3
4
5
2
3
(a) Develop a mixed-integer programming model that could be used to help Martin-Beck determine which new plant or plants to open in order
to satisfy anticipated demand. Solve the model and answer the following questions. What is the optimal cost?
$ 104800
What is the optimal set of plants to open?
Detroit & Toledo
(b) Using equation 13.1, find a second-best solution. What is the optimal set of plants to open?
Denver
What is the increase in cost versus the best solution from part (a)?
$ 120000
Transcribed Image Text:The shipping cost per unit from each plant to each distribution center is as follows: Plant Site Detroit Toledo Denver Kansas City St. Louis Boston 5 4 9 10 8 Distribution Centers Atlanta 2 3 7 4 4 Houston 3 4 5 2 3 (a) Develop a mixed-integer programming model that could be used to help Martin-Beck determine which new plant or plants to open in order to satisfy anticipated demand. Solve the model and answer the following questions. What is the optimal cost? $ 104800 What is the optimal set of plants to open? Detroit & Toledo (b) Using equation 13.1, find a second-best solution. What is the optimal set of plants to open? Denver What is the increase in cost versus the best solution from part (a)? $ 120000
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