3. Tri-County Utilities, Inc. supplies natural gas to customers in three-county area. The company purchases purchases natiural gas from two companies: Southern Gas and Northwest Gas. Deman 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 quanities 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:ToFrom Hamilton Butler ClermontSouthern Gas 10 20 15Northwest Gas 12 15 18a. Develop a network representation of this problem.b. Develop a linear programming model that can be used to determine the plan that will minimize total distribution costs.c. Describe the distribution plan and show the total distribution cost.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?

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