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, 500 units; Butler County, 250 units; and Clermont County, 310 units. Contracts to provide the following quantities have been written: Southern Gas, 550 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 Southern Gas 12 19 16 Northwest Gas 14 15 20 (5 points each) a. 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?