# 1 x 11 1 x 12 1 x 13 500 1 x 21 1 x 22 1 x 23 400 1 x

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1 x 11 + 1 x 12 + 1 x 13 500 1 x 21 + 1 x 22 + 1 x 23 400 1 x 11 + 1 x 21 = 400 1 x 12 + 1 x 22 = 200 1 x 13 + 1 x 23 = 300 x ij ≥ 0 for all i , Model (iii) j
c. Describe the distribution plan and show the total distribution cost. If your answer is zero enter "0". Amount Cost Southern - Hamilton 200 \$ 2,000 Southern - Butler 0 0 Southern - Clermont 300 4,500 Northwest - Hamilton 200 2,400 Northwest - Butler 200 3,000 Northwest - Clermont 0 0 Total Cost \$ 11,900
d. Recent residential and industrial growth in Butler County has the potential for increasing demand by as much as 100 units. Which supplier should Tri-County contract with to supply the additional capacity? If your answer is zero enter "0". Amount Cost Southern - Hamilton 300 \$ 3,000 Southern - Butler 0 0 Southern - Clermont 300 4,500 Northwest - Hamilton 100 1,200 Northwest - Butler 300 4,500 Northwest - Clermont 0 0 Total Cost \$ 13,200 From the new solution we see that Tri-County should contract with Gas for the additional 100 units. Feedback Check My Work Correct Post-Submission a. b. Let amount shipped from supply node i to demand node j . Min s.t. 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 Southern
From the new solution we see that Tri-County should contract with Southern Gas for the additional 100 units. Solution Problem 6-03 Tri-County Utilities, Inc., supplies natural gas to customers in a three-county area. The company purchases natural gas from two companies: Southern Gas and Northwest Gas. Demand forecasts for the coming winter season are as follows: Hamilton County, 400 units; Butler County, 200 units; and Clermont County, 300 units. Contracts to provide the following quantities have been written: Southern Gas, 500 units; and Northwest Gas, 400 units. Distribution costs for the counties vary, depending upon the location of the suppliers. The distribution costs per unit (in thousands of dollars) are as follows: To From Hamilton Butler Clermont Southern Gas 10 20 15 Northwest Gas 12 15 18