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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

a. Develop a linear programming model that can be used to determine the plan that will minimize total distribution costs. Let x_ij = amount shipped from supply node i to demand node j.

b. Describe the distribution plan and show the total distribution cost.

	Amount	Cost
Southern - Hamilton
Southern - Butler
Southern - Clermont
Northwest - Hamilton
Northwest - Butler
Northwest - Clermont
Total Cost

c. 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?

	Amount	Cost
Southern - Hamilton
Southern - Butler
Southern - Clermont
Northwest - Hamilton
Northwest - Butler
Northwest - Clermont
Total Cost

From the new solution we see that Tri-County should contract with Gas for the additional 100 units.