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Chemco is based in Canada. Chemco produces one chemical, chemical X by applying pro- cesses to three inputs A, B, and C. Chemco has two production processes with the following characteristics (amounts of chemical in ounces): Input A Input B Input C Output X Process 1 Process 2 3 0 1 3 6 4 0 2 That is, we can obtain 2 ounces of output X by inputting both 3 ounces of input A and 1 ounce of input B. Chemco must meet a demand of 1000 ounces of product X. Chemco imports all of its raw materials, A, B, C. The Canadian government is considering three possible chemical tariff packages. In response to the package chosen, Chemco's suppliers would change their prices. The resulting per ounce prices are given below.

Chemco is based in Canada. Chemco produces one chemical, chemical X by applying pro- cesses to three inputs A, B, and C. Chemco has two production processes with the following characteristics (amounts of chemical in ounces): Input A Input B Input C Output X Process 1 Process 2 3 0 1 3 6 4 0 2 That is, we can obtain 2 ounces of output X by inputting both 3 ounces of input A and 1 ounce of input B. Chemco must meet a demand of 1000 ounces of product X. Chemco imports all of its raw materials, A, B, C. The Canadian government is considering three possible chemical tariff packages. In response to the package chosen, Chemco's suppliers would change their prices. The resulting per ounce prices are given below.

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 68P
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Chemco is based in Canada. Chemco produces one chemical, chemical X by applying pro- cesses to three inputs A, B, and C. Chemco has two production processes with the following characteristics (amounts of chemical in ounces): Input A Input B Input C Output X Process 1 Process 2 3 0 1 3 0 6 2 4 That is, we can obtain 2 ounces of output X by inputting both 3 ounces of input A and 1 ounce of input B. Chemco must meet a demand of 1000 ounces of product X. Chemco imports all of its raw materials, A. B. C. The Canadian government is considering three possible chemical tariff packages. In response to the package chosen, Chemco's suppliers would change their prices. The resulting per ounce prices are given below. 1 2 3 Price per ounce Tariff Package Chemical A Chemical B Chemical C $3 $5 $1 $3 $2 $7 $4 $10 $12 Suppose Chemco must commit to its production process before the tariff package is known. Formulate an LP to minimize Chemco's worst case raw materials cost over all outcomes of the tariff package, i.e. minimize the cost of the most harmful tariff package being implemented. It may help to first state this problem using a maximum, but note that taking a maximum is nonlinear.
Transcribed Image Text:Chemco is based in Canada. Chemco produces one chemical, chemical X by applying pro- cesses to three inputs A, B, and C. Chemco has two production processes with the following characteristics (amounts of chemical in ounces): Input A Input B Input C Output X Process 1 Process 2 3 0 1 3 0 6 2 4 That is, we can obtain 2 ounces of output X by inputting both 3 ounces of input A and 1 ounce of input B. Chemco must meet a demand of 1000 ounces of product X. Chemco imports all of its raw materials, A. B. C. The Canadian government is considering three possible chemical tariff packages. In response to the package chosen, Chemco's suppliers would change their prices. The resulting per ounce prices are given below. 1 2 3 Price per ounce Tariff Package Chemical A Chemical B Chemical C $3 $5 $1 $3 $2 $7 $4 $10 $12 Suppose Chemco must commit to its production process before the tariff package is known. Formulate an LP to minimize Chemco's worst case raw materials cost over all outcomes of the tariff package, i.e. minimize the cost of the most harmful tariff package being implemented. It may help to first state this problem using a maximum, but note that taking a maximum is nonlinear.
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