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Aire-Co produces home dehumidifiers at two different plants in Atlanta and Phoenix. The per unit cost of production in Atlanta and Phoenix is $400 and $360, respectively. Each plant can produce a maximum of 300 units per month. Inventory holding costs are assessed at $30 per unit in beginning inventory each month. Aire-Co estimates the demand for its product to be 300, 400, and 500 units, respectively, over the next 3 months. Aire-Co wants to be able to meet this demand at minimum cost. a. Formulate an LP model for this problem (write out the objective function and constraints). b. Implement your model in a spreadsheet and solve it. c. What is the optimal solution? d. How does the solution change if each plant required to produce at least 50 units per month? e. How does the solution change if each plant is required to produce at least 100 units per month?

Aire-Co produces home dehumidifiers at two different plants in Atlanta and Phoenix. The per unit cost of production in Atlanta and Phoenix is $400 and $360, respectively. Each plant can produce a maximum of 300 units per month. Inventory holding costs are assessed at $30 per unit in beginning inventory each month. Aire-Co estimates the demand for its product to be 300, 400, and 500 units, respectively, over the next 3 months. Aire-Co wants to be able to meet this demand at minimum cost. a. Formulate an LP model for this problem (write out the objective function and constraints). b. Implement your model in a spreadsheet and solve it. c. What is the optimal solution? d. How does the solution change if each plant required to produce at least 50 units per month? e. How does the solution change if each plant is required to produce at least 100 units per month?

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section: Chapter Questions
Problem 107P
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Aire-Co produces home dehumidifiers at two different plants in Atlanta and Phoenix. The per unit cost of production in Atlanta and Phoenix is $400 and $360, respectively. Each plant can produce a maximum of 300 units per month. Inventory holding costs are assessed at $30 per unit beginning inventory each month. Aire-Co estimates the demand for its product to be 300, 400, and 500 units, respectively, over the next 3 months. Aire-Co wants to be able to meet this demand at minimum cost. a. Formulate an LP model for this problem (write out the objective function and constraints). b. Implement your model in a spreadsheet and solve it. c. What is the optimal solution? d. How does the solution change if each plant required to produce at least 50 units per month? e. How does the solution change if each plant is required to produce at least 100 units per month?
Transcribed Image Text:Aire-Co produces home dehumidifiers at two different plants in Atlanta and Phoenix. The per unit cost of production in Atlanta and Phoenix is $400 and $360, respectively. Each plant can produce a maximum of 300 units per month. Inventory holding costs are assessed at $30 per unit beginning inventory each month. Aire-Co estimates the demand for its product to be 300, 400, and 500 units, respectively, over the next 3 months. Aire-Co wants to be able to meet this demand at minimum cost. a. Formulate an LP model for this problem (write out the objective function and constraints). b. Implement your model in a spreadsheet and solve it. c. What is the optimal solution? d. How does the solution change if each plant required to produce at least 50 units per month? e. How does the solution change if each plant is required to produce at least 100 units per month?
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