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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: From To Hamilton Butler Clermont 10 20 15 12 15 18 Southern Gas Northwest Gas a. Choose the correct network representation of this problem. (0) Hamilton 10 300 12 Hamilton 12 400 10 South Southern 900 500 15 15 Butler 2 Butler 2 200 20 Norte Northwest 400 400 15 40 Clement FIE 300 Clermont 3 13 (ii) (iv) Hum 400 Handton 1 300 M 500 Southern 500 20 15 Southam 1 20 12 12 Butler 2 200 35 15 15 400 Norte 2 400 Northwest 2 13 300 Clermont 400 b. Develop a linear programming model that can be used to determine the plan that will minimize total distribution costs. If the constant is "1" it must be entered in the box. Let xij = amount shipped from supply node i to demand node j. *11+ x12 + x13 + 1 +1 Min x21+ X22+ x23 s.t. x11]+ + x12 + x13