$293$Problems$3.$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: