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# Reading Questions - subject to source to game Z =...

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maximize Z = \$120x 1 + \$85x 2 + \$105x 3 + \$140x 4 + \$70x 5 subject to: (budget restriction year 1) \$55x 1 + \$45x 2 + \$60x 3 + \$50x 4 + \$30x 5 \$150 (budget restriction year 2) \$40x 1 + \$35x 2 + \$25x 3 + \$35x 4 + \$30x 5 \$110 (budget restriction year 3) \$25x 1 + \$20x 2 + \$30x 4 \$60 (store choice) x 3 + x 4 1 (0-1) x i = 0 or 1 + 405y 1 + 390y 2 + 450y 3 + 368y 4 + 520y 5 + 465y 6 Constraints: subject to: (shipped from 1 only if 1 chosen) x 1A + x 1B + x 1C - 11.2y 1 0 (shipped from 2 only if 2 chosen) x 2A + x 2B + x 2C -10.5y 2 0 (shipped from 3 only if 3 chosen) x 3A + x 3B + x 3C - 12.8y 3 0 (shipped from 4 only if 4 chosen) x 4A + x 4B + x 4C - 9.3y 4 0 (shipped from 5 only if 5 chosen) x 5A + x 5B + x 5C - 10.8y 5 0 (shipped from 6 only if 6 chosen) x 6A + x 6B + X 6C - 9.6y 6 0 (capacity constraint, plant A) x 1A + x 2A + x 3A + x 4A + x 5A + x 6A = 12 (capacity constraint, plant B) x 1B + x 2B + x 3B + x 4B + x 5B + x 6B = 10 (capacity constraint, plant C) x 1C + x 2C + x 3C + x 4C + x 5C + x 6C = 14 (non-negativity) x ij 0 (binary) y i = 0 or 1 subject to: (Atlanta) x 1 + x 3 + x 8 1 (Boston) x 2 + x 10 1 (Charlotte) x 1 + x 3 + x 11 1 (Cincinnati) x 4 + x 5 + x 6 + x 8 + x 10 1 (Detroit) x 4 + x 5 + x 6 + x 7 + x 10 1 (Indianapolis) x 4 + x 5 + x 6 + x 7 + x 8 + x 12 1 (Milwaukee) x 5 + x 6 + x 7 1 (Nashville) x 1 + x 4 + x 6 + x 8 + x 12 1 (New York) x 2 + x 9 + x 11 1 (Pittsburgh) x 4 + x 5 + x 10 + x 11 1 (Richmond) x 3 + x 9 + x 10 + x 11 1 (St Louis) x 6 + x 8 + x 12 1 (binary) x ij = 0 or 1 Objective Function: minimize Z = \$6x 1A + 8x 1B + 10x 1C + 7x 2A + 11x 2B + 11x 2C + 4x 3A + 5x 3B + 12x 3C Constraints: subject to: (supply elevator 1) x 1A + x 1B + x 1C = 150 (supply elevator 2) x 2A + x 2B + x 2C = 175 (supply elevator 3) x 3A + x 3B + x 3C = 275 (demand mill A) x 1A + x 2A + x 3A = 200 (demand mill B) x 1B + x 2B + x 3B = 100 (demand mill C) x 1C + x 2C + x 3C = 300 (non-negativity) x ij 0 source to game Z = 210x AR + 90x AA + 180x AD + 160x AC + 100x BR + 70x BA + 130x BD + 200x BC + 175x CR + 105x CA + 140x CD + 170x CC + 80x DR + 65x DA + 105x DD + 120x DC cial team A) x AR + x AA + x AD + x AC = 1 – Ref A is only reffing 1 game cial team B) x BR + x BA + x BD + x BC = 1 cial team C) x CR + x CA + x CD + x CC = 1 cial team D) x DR + x DA + x DD + x DC = 1 and Raleigh) x AR + x BR + x CR + x DR = 1 – Game R only has one ref mand Atlanta) x AA + x BA + x CA + x DA = 1 and Durham) x AD + x BD + x CD + x DD = 1 and Clemson) x AC + x BC + x CC + x DC = 1 non-negativity) x ij 0 Reading Questions Chapter 5 What are the three different kinds of integer programming models and how do they differ? Total Integer Model – all the decision variables are required to have integer solution values Ex: owner buying presses and lathes 0-1 Integer Model – all the decision variables have integer values of zero or one (binary values; choice selection and rejection) Ex: have to choose which new rec facilities to add to a community Mixed Integer Model – some of the decision variables (but not all) are required to have integer solutions Ex: buying condos and bonds need to be integer, but buying land does not need to be because you can buy half acres What is a mutually exclusive constraint?

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