Math_540_Assignment 4 part 3

# Math_540_Assignment 4 part 3 - 1 There are 18 decision...

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Unformatted text preview: 1) There are 18 decision variables, because there are 6 plants and 3 waste disposal sites: Objective Function: Minimize Z = 12 1 A x + 15 1 B x + 17 1 C x + 14 2 A x + 9 2 B x + 10 2 C x + 13 3 A x + 20 3 B x +11 3 C x +17 4 A x +16 4 B x +19 4 C x +7 5 A x +14 5 B x +12 5 C x +22 6 A x +16 6 B x +18 6 C x Supply Constraints: 1 A x + 1 B x + 1 C x = 35 2 A x + 2 B x + 2 C x = 26 3 A x + 3 B x + 3 C x = 42 4 A x + 4 B x + 4 C x = 53 5 A x + 5 B x + 5 C x = 29 6 A x + 6 B x + 6 C x = 38 Demand Constraints: 1 A x + 2 A x + 3 A x + 4 A x + 5 A x + 6 A x ≤ 65 1 B x + 2 B x + 3 B x + 4 B x + 5 B x + 6 B x ≤ 80 1 C x + 2 C x + 3 C x + 4 C x + 5 C x + 6 C x ≤ 105 The linear programming model: Minimize Z = 12 1 A x + 15 1 B x + 17 1 C x + 14 2 A x + 9 2 B x + 10 2 C x + 13 3 A x + 20 3 B x +11 3 C x +17 4 A x +16 4 B x +19 4 C x +7 5 A x +14 5 B x +12 5 C x +22 6 A x +16 6 B x +18 6 C x Subject to 1 A x + 1 B x + 1 C x = 35 2 A x + 2 B x + 2 C x = 26 3 A x + 3 B x + 3 C x = 42 4 A x + 4 B x + 4 C x = 53 5 A x + 5 B x + 5 C x = 29 6 A x + 6 B x + 6 C x = 38 1 A x + 2 A x + 3 A x + 4 A x + 5 A x + 6 A x ≤ 65 1 B x + 2 B x + 3 B x + 4 B x + 5 B x + 6 B x ≤ 80 1 C x + 2 C x + 3 C x + 4 C x + 5 C x + 6 C x ≤ 105 ij x ≥ 2) Estimated Shipping Cost (\$ per barrel) Plant Waste Disposal Sites Whitewater Los Canos Duras Kingsport 12 15 17 Danville 14 9 10 Macon 13 20 11 Selma 17 16 19 Columbus 7 14 12 Allentown 22 16 18 Plant Waste Disposal Sites Supply Waste Shipped Whitewater Los Canos Duras Kingsport 35.0 0.0 0.0 35.0 35.0 Danville 0.0 0.0 26.0 26.0 26.0 Macon 0.0 0.0 42.0 42.0 42.0 Selma 1.0 52.0 0.0 53.0 53.0 Columbus 29.0 0.0 0.0 29.0 29.0 Allentown 0.0 28.0 10.0 38.0 38.0 Waste Received 65.0 80.0 105.0 223.0 Waste Disposed 65.0 80.0 78.0 223.0 Cost= \$ 2,822 Optimal Solution From To Shipment unit Cost per unit Shipment cost Kingsport Whitewater 35 \$12 \$420 Danville...
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Math_540_Assignment 4 part 3 - 1 There are 18 decision...

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