Tri-County   Utilities, Inc., supplies natural gas to consumers 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      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 upon the location of the suppliers.   The distribution costs per   unit (in thousands of dollars) are as follows:      From Hamilton To   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 to determine the plan that will minimize   total distribution costs.   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 100 units. Which supplier should    Tri-County contract with to   supply the additional capacity?    

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