### Describe distribution plan also show total distribution cost

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Q. Tri-county utilities, Inc supplies natural gas to customers in a three-county area. Company purchases natural gas from two companies; Southern gas also northwest gas. Demand forecasts for coming winter season are Hamilton County, 400 units; Butler County, 200 units also Clermont County, 300 units. Contracts to provide subsequent quantities have been written: So RN gas 500 units; also northwest gas, 400 units. Distribution cost for counties vary, depending upon location of supplies. distributions cost per unit are as follows

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 which can be used to determine plan which will minimize total distribution costs.

c) Describe distribution plan also Show total distribution cost.

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