# Ch07 - 1 MP CHAPTER 7 SOLUTIONS SECTION 7.1 1 Warehouse 1...

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MP CHAPTER 7 SOLUTIONS SECTION 7.1 1. Cust. 1 Cust. 2 Cust. 3 Warehouse 1 15 35 25 40 Warehouse 2 10 50 40 30 Shortage 90 80 110 20 30 30 30 2. C1 C2 C3 DUMMY W1 15 35 25 0 40 W2 10 50 40 0 30 W1 EXTRA 115 135 125 0 20 W2 EXTRA 110 150 140 0 20 30 30 30 20 1

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3. M1 M2 M3 M4 M5 M6 M7 1R 7 8 9 10 11 12 0 200 1O 11 12 13 14 15 16 0 100 2R M 7 8 9 10 11 0 200 2O M 11 12 13 14 15 0 100 3R M M 7 8 9 10 0 200 3O M M 11 12 13 14 0 100 4R M M M 7 8 9 0 200 4O M M M 11 12 13 0 100 5R M M M M 7 8 0 200 5O M M M M 11 12 0 100 6R M M M M M 7 0 200 6O M M M M M 11 0 100 200 260 240 340 190 150 420 4a. Let x ij = number of tons of steel j produced at plant i. Then the supply at plant 1 is 40(60)/20 = 120 tons, the supply at plant 2 is 40(60)/16 = 150 tons, and the supply at plant 3 is 40(60)/15 = 160 tons. We obtain the following balanced transportation problem: Steel 1 Steel 2 Steel 3 Dummy Plant 1 60 40 28 0 120 Plant 2 50 30 30 0 150 Plant 3 43 20 20 0 160 100 100 100 130 4b. In this situation we cannot define the production capacity of a plant in terms of tons of steel produced; this is because, even if produced at the same plant, each type of steel requires a different amount of time to produce. For instance, an attempt to determine the plant 1 supply constraint would yield 2
15x 11 + 12x 12 + 15x 13 <_2400, and this constraint is not of the required form for a supply constraint. (x 11 + x 12 + x 13 <_ plant 1 supply.) 5. Month 1 Month 2 Daisy 800 720 0 5 Laroach 710 750 0 5 3 4 3 6. Vendor Salary Personnel Dummy Site 1 5 4 2 0 10000 Site 2 3 4 5 0 6000 5000 5000 5000 1000 7. This is a maximization problem so number in each cell is revenue, not a cost. Cliff Blake Alexis Site 1 1,000 900 1,100 100,000 Site 2 2,000 2,200 1,900 100,000 Dummy 0 0 0 40,000 80,000 80,000 80,000 8. The profit earned from shipping a barrel is as follows: From Field 1 to England: 6 - 3 - 1 = \$2 From Field 1 to Japan: 6.5 - 3 - 2 = \$1.50 From Field 2 to England: 6 - 2 - 2 = \$2 From Field 2 to Japan: 6.5 - 2 - 1 = \$3.50 Since all types of shipments are profitable, we know that the optimal solution will ship 40 million barrels to England and 30 million barrels to Japan. Thus we can add a dummy demand of 20 million to balance the problem yielding the following balanced transp. problem: (supplies and demands are in millions of barrels) England Japan Dummy 3

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Field 1 2 1.5 0 40 Field 2 2 3.5 0 50 40 30 20 10. Let xij = number of hours auditor i spends on project j. Then the appropriate (maximization) tableau is Project 1 Project 2 Project 3 Dummy Aud 1 120 150 190 0 160 Aud 2 140 130 120 0 160 Aud 3 160 140 150 0 160 130 140 160 50 11. Let x ij =Number of tons of Type i pulp that are processed in an effort to make Type j paper. Then the following balanced transp. tableau represents the problem (1)RNP (2)RUP (3)RCP Dummy (1) NP 13 M 14 0 500 (2) UCP 12 9 14 0 200 (3) CP M 14 12 0 300 312.5 352.94 166.67 167.89 Costs are expressed in terms of x ij . Demand for each type of recycled paper must be expressed in terms of the number of tons of input pulp required to produce the required recycled paper. For example, 250 tons of recycled newsprint pulp (Demand Pt. 1) is needed. Each ton of pulp that is used to meet demand for recycled newsprint yields (1-.2) =.8 tons of recycled newsprint. Thus 250/.8=312.5 tons of pulp must be processed to meet demand for recycled newsprint pulp.
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