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Hillier2-Ch2-Assignment-1b

Hillier2-Ch2-Assignment-1b - MGTM3100 Assignment#1 2.7 a A...

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MGTM3100 – Assignment #1 2.7 a) 1 2 3 4 5 6 7 8 9 10 A B C D E F Product A Product B Unit Profit $3,000 $2,000 Resource Resource Used Available Resource Q 2 1 2 Š 2 Resource R 1 2 2 Š 2 Resource S 3 3 4 Š 4 Product A Product B Total Profit Units Produced 0.667 0.667 $3,333.33 Resource Usage per Unit Produced b) Let A = units of product A produced B = units of product B produced Maximize P = $3,000 A + $2,000 B , subject to 2 A + B ≤ 2 A + 2 B ≤ 2 3 A + 3 B ≤ 4 and A ≥ 0, B ≥ 0. c) Optimal Solution = ( A , B ) = ( x 1 , x 2 ) = (0.667, 0.667). P = $3333.33. 2.9 a) objective function Z = x 1 + 2 x 2 functional constraints x 1 + x 2 ≤ 5 x 1 + 3 x 2 ≤ 9 nonnegativity constraints x 1 ≥ 0, x 2 ≥ 0 2-1
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b & e) 1 2 3 4 5 6 7 8 9 A B C D E F x 1 x 2 Unit Profit 1 2 Resource Resource Used Available Resource 1 1 1 5 Š 5 Resource 2 1 3 9 Š 9 x 1 x 2 Total Profit Decision 3 2 7 Resource Usage c) Yes. d) No. f) Optimal Solution: ( x 1 , x 2 ) = (3, 2) and Z = 7. 2.10 a) objective function Z = 3 x 1 + 2 x 2 functional constraints 3 x 1 + x 2 ≤ 9 x 1 + 2 x 2 ≤ 8 nonnegativity constraints x 1 ≥ 0, x 2 ≥ 0 b & f) 1 2 3 4 5
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