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Problem $10-03$

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 N Gas. Demand forecasts for the coming winter season are as follows: Hamilton County, $400$ units; Butler County, $200$ units; and Clermont County, $300$ units. Cont provide the following quantities have been written: Southern Gas, $500$ units; and Northwest Gas, $400$ units. Distribution costs for the counties vary, depending up location of the suppliers. The distribution costs per unit $($in thousands of dollars$)$ are as follows:

From

Southem Gas

Northwest Gas

Hamilton

$10$

$12$

To

Butler

$20$

$15$

Clermont

$15$

$18$

a$.$ Choose the correct network representation of this problem.

$($i$)$

$($ii$)$

Previous $($for part B$)$Develope a linear programming model that can be used to detwrmine the plan that will minimize total distribution costs. Let xij$=$amount shipped from supply node i to demand node j$.($For part C$)$ describe the distribution plan and show the toral distribution cost.