Homework 2 Set Chapter Solutions

Homework 2 Set Chapter Solutions - Solutions Odd Chapter 6...

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Solutions: Odd Chapter 6 1. The network model is shown. Phila. New Orleans Boston Columbus Dallas Atlanta 5000 3000 7 5 2 1 2 6 6 2 1400 2000 3200 1400 6.3 a. 1 Hamilton 3 Clermont 2 Butler 2 Northwest 1 Southern 10 20 15 12 15 18 400 200 300 500 400 b. Let x ij = amount shipped from supply node i to demand node j .

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Min 10 x 11 + 20 x 12 + 15 x 13 + 12 x 21 + 15 x 22 + 18 x 23 s.t. x 11 + x 12 + x 13 500 x 21 + x 22 + x 23 400 x 11 + x 21 = 400 x 12 + x 22 = 200 x 13 + x 23 = 300 x ij 0 for all i , j c. Optimal Solution Amount Cost Southern - Hamilton 200 \$ 2000 Southern - Clermont 300 4500 Northwest - Hamilton 200 2400 Northwest - Butler 200 3000 Total Cost \$11,900 d. To answer this question the simplest approach is to increase the Butler County demand to 300 and to increase the supply by 100 at both Southern Gas and Northwest Gas. The new optimal solution is: Amount Cost Southern - Hamilton 300 \$ 3000 Southern - Clermont 300 4500 Northwest - Hamilton 100 1200 Northwest - Butler 300 4500 Total Cost \$13,200 From the new solution we see that Tri-County should contract with Southern Gas for the additional 100 units.
6.9 9. a.

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