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

Required:
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.