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 $175,000 Annual Fixed Cost Annual Capacity 40,000 $300,000 $375,000 $500,000 10,000 20,000 30,000 The company's long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows: Distribution Center Annual Demand Boston 30,000 Atlanta 20,000 Houston 20,000 The shipping cost per unit from each plant to each distribution center is as follows: Distribution Centers Plant Site Detroit Boston Atlanta Houston 5 2 3 Toledo 4 3 4 Denver 9 7 5 Kansas City 10 4 2 St. Louis 8 4 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? $ 860000 What is the optimal set of plants to open? Kansas City (b) Using equation 12.1, find a second-best solution. What is the optimal set of plants to open? - Select your answer - What is the increase in cost versus the best solution from part (a)?
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 $175,000 Annual Fixed Cost Annual Capacity 40,000 $300,000 $375,000 $500,000 10,000 20,000 30,000 The company's long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows: Distribution Center Annual Demand Boston 30,000 Atlanta 20,000 Houston 20,000 The shipping cost per unit from each plant to each distribution center is as follows: Distribution Centers Plant Site Detroit Boston Atlanta Houston 5 2 3 Toledo 4 3 4 Denver 9 7 5 Kansas City 10 4 2 St. Louis 8 4 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? $ 860000 What is the optimal set of plants to open? Kansas City (b) Using equation 12.1, find a second-best solution. What is the optimal set of plants to open? - Select your answer - What is the increase in cost versus the best solution from part (a)?
Chapter1: Financial Statements And Business Decisions
Section: Chapter Questions
Problem 1Q
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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
$175,000
Annual Fixed Cost
Annual Capacity
40,000
$300,000
$375,000
$500,000
10,000
20,000
30,000
The company's long-range planning group developed forecasts of the anticipated annual demand at the distribution centers as follows:
Distribution Center
Annual Demand
Boston
30,000
Atlanta
20,000
Houston
20,000
Transcribed Image Text:The shipping cost per unit from each plant to each distribution center is as follows:
Distribution Centers
Plant Site
Detroit
Boston
Atlanta
Houston
5
2
3
Toledo
4
3
4
Denver
9
7
5
Kansas City
10
4
2
St. Louis
8
4
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?
$ 860000
What is the optimal set of plants to open?
Kansas City
(b) Using equation 12.1, find a second-best solution. What is the optimal set of plants to open?
- Select your answer -
What is the increase in cost versus the best solution from part (a)?
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