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hw5Solution

# hw5Solution - INFO 372 Homework 6 Due date Tuesday May 2 at...

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Solution: HW 5 6.3-5 (8 th edition) 4.1.(8 th edition) Only part b) (no need to show that part b) produces the same result as part a)

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3 Carco manufactures cars and trucks. Each car contributes \$300 to profit and each truck, \$400. The resources required to manufacture a car and truck are shown in the table below. Each day, Carco can rent up to 98 type 1 machines at a cost of \$50 per machine. At present, the company has 73 type 2 machines and 260 tons of steel available. Marketing considerations dictate that at least 88 cars and at least 26 trucks be produced. Let X1 – number cars produce daily X2 – number of trucks produced daily M1 – type 1 machines rented daily Days on Type 1 Machine Days on Type 2 Machine Tons of steel Car 0.8 0.6 2 Truck 1 0.7 3 To maximize profit, Carco should solve the following LP (it’s okay to get fractional solutions – this is only for planning purposes). Max 300 X1 + 400 X2 – 50 M1 Subject to: 0.8 X1 + X2 – M1 <= 0; M1 <= 98; 0.6 X1 + 0.7 X2 <= 73; 2 X1 + 3 X2 <= 260; X1 >= 88; X2 >= 26; X1 >=0; X2 >=0; a) Formulate the dual problem. b) Solve the problem using MPL. Use the MPL output to answer the questions below.
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