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6. Lab Week 6 Problem Solutions

6. Lab Week 6 Problem Solutions - Lab Week 6 Problem...

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Lab Week 6 Problem Solutions CHAPTER 5 DISTRIBUTION AND NETWORK FLOW MODELS 1. 1a. Let Xij = the number of units shipped from plant i to warehouse j. Where i = A, B, C j= 1, 2, 3 Objective Function (Minimize): Min. Z = 50X A1 + 32X A2 + 40X A3 + 16X B1 + 30X B2 + 20X B3 + 35X C1 + 28X C2 + 42X C3 Subject to Supply Constraints: Non-negativity Constraints X A1 + X A2 + X A3 = 700 All variables ≥0 X B1 + X B2 + X B3 = 200 X C1 + X C2 + X C3 = 200 Demand Constraints: X A1 + X B1 + X C1 = 300 X A2 + X B2 + X C2 = 400 X A3 + X B3 + X C3 = 400
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1b. When using solver, make sure “assume linear model” and “assume non-negativity” are checked under the options menu. Excel formatting:
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1c. To make sure route 3-A is unacceptable, change the cost to a very high number (e.g., ten times the next highest cost). Note the cost of $500 from plant A to warehouse 3. The solver constraints are the same.
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15. 15a. Objective Function (minimize cost): Min. Z = 9X 13 + 11X 14 + 10X 23 + 12X 24 + 8X 35 + 4X 36 + 6X 45 + 7X 46 Subject to Supply Constraints: Non-Negativity Constraint: X 13 + X 14 = 200 All variables ≥ 0 X 23 + X 24 = 300 Transshipment Constraints : X
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