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Klein Chemicals, Inc., produces a special oil-based material that is currently in short supply. Four of Klein's customers have already placed orders that together exceed the combined capacity of Klein's two plants. Klein's management faces the problem of deciding how many units it should supply to each customer. Because the four customers are in different industries, different prices can be charged because of the various industry pricing structures. However, slightly different production costs at the two plants and varying transportation costs between the plants and customers make a "sell to the highest bidder" strategy unacceptable. After considering price, production costs, and transportation costs, Klein established the following profit per unit for each plant-customer alternative. Plant Clifton Springs Danville Plant Clifton Springs 1 Danville 2 D₂ n 3 1 D₂2 D₂ D4 $34 $32 $40 $38 $32 The plant capacities and customer orders are as follows. Customer $34 $30 $28 Capacity (units) 5,000 3,000 4 Distributor Orders (units) D₂ D₂ 2,000 5,000

Klein Chemicals, Inc., produces a special oil-based material that is currently in short supply. Four of Klein's customers have already placed orders that together exceed the combined capacity of Klein's two plants. Klein's management faces the problem of deciding how many units it should supply to each customer. Because the four customers are in different industries, different prices can be charged because of the various industry pricing structures. However, slightly different production costs at the two plants and varying transportation costs between the plants and customers make a "sell to the highest bidder" strategy unacceptable. After considering price, production costs, and transportation costs, Klein established the following profit per unit for each plant-customer alternative. Plant Clifton Springs Danville Plant Clifton Springs 1 Danville 2 D₂ n 3 1 D₂2 D₂ D4 $34 $32 $40 $38 $32 The plant capacities and customer orders are as follows. Customer $34 $30 $28 Capacity (units) 5,000 3,000 4 Distributor Orders (units) D₂ D₂ 2,000 5,000

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Klein Chemicals, Inc., produces a special oil-based material that is currently in short supply. Four of Klein's customers have already placed orders that together exceed the combined capacity of Klein's two plants. Klein's management faces the problem of deciding how many units it should supply to each customer. Because the four customers are in different industries, different prices can be charged because of the various industry pricing structures. However, slightly different production costs at the two plants and varying transportation costs between the plants and customers make a "sell to the highest bidder" strategy unacceptable. After considering price, production costs, and transportation costs, Klein established the following profit per unit for each plant-customer alternative. Plant Clifton Springs Danville Plant Clifton Springs Danville Clifton Springs-D₁ Clifton Springs-D₂ Clifton Springs-D3 Clifton Springs-D4 2 The plant capacities and customer orders are as follows. Danville-D₁ Danville-D₂ Danville-D3 Danville-D4 D1 Total Cost D₂ $32 $34 $32 $40 $34 $30 $28 Customer 2 Capacity (units) 2000 5,000 3,000 3 D3 D4 Units X $ (a) How many units should each plant produce for each customer to maximize profits? Optimal Solution $ 64,000 $ $ $ $ $38 tA $ Cost 4 Distributor Orders (units) D₁ D₂ D3 D4 2,000 X 5,000 3,000 2,000
Transcribed Image Text:Klein Chemicals, Inc., produces a special oil-based material that is currently in short supply. Four of Klein's customers have already placed orders that together exceed the combined capacity of Klein's two plants. Klein's management faces the problem of deciding how many units it should supply to each customer. Because the four customers are in different industries, different prices can be charged because of the various industry pricing structures. However, slightly different production costs at the two plants and varying transportation costs between the plants and customers make a "sell to the highest bidder" strategy unacceptable. After considering price, production costs, and transportation costs, Klein established the following profit per unit for each plant-customer alternative. Plant Clifton Springs Danville Plant Clifton Springs Danville Clifton Springs-D₁ Clifton Springs-D₂ Clifton Springs-D3 Clifton Springs-D4 2 The plant capacities and customer orders are as follows. Danville-D₁ Danville-D₂ Danville-D3 Danville-D4 D1 Total Cost D₂ $32 $34 $32 $40 $34 $30 $28 Customer 2 Capacity (units) 2000 5,000 3,000 3 D3 D4 Units X $ (a) How many units should each plant produce for each customer to maximize profits? Optimal Solution $ 64,000 $ $ $ $ $38 tA $ Cost 4 Distributor Orders (units) D₁ D₂ D3 D4 2,000 X 5,000 3,000 2,000
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