1. 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: To From Hamilton Butler Clermont Southern Gas 10 20 15 Northwest Gas 12 15 18

a. Develop a network representation of this problem. b. Develop a linear programming model that can be used...