Tri-County Utilities, Inc. supplies natural gas to customers in 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 Clermont County 300 Units Contracts to provide the following quantities have been written: Southern Gas 500 Units Northwest Gas 400 Units Distribution costs for the counties vary, depending on the location and suppliers. The distribution costs per unit (in thousands of dollars) are as follows: From Hamilton Butler Clermont Southern Gas 10 20 15 Northwest Gas 12 15 18 a) Develop network representation of the problem (and draw a graph). b) Develop a linear programming model that can be used to determine the plan that will minimize total distribution cost. 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 10 units. Which supplier should Tri-Company contract with to supply the additional capacity?