Tri-county utilities, inc supplies natural gas to customers in a three-county area. the campany purchases natural gas from two companies; southern gas and northwest gas. demand forecasts for the coming winter season are hamilton coutny. 400 units; butler county, 200 units; and clermont county, 300 units. contracts to provide the following quantities have been written: sothern gas 500 units; and northwest gas, 400 units. distribution cost for the counties vary, depending upon the location of the supplies. The 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 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.