Tri-County Utilities, Inc., supplies natural gas to customers in a three-county area. The company purchases natural gas

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Tri-County Utilities, Inc., supplies natural gas to customers ina three-county area. The company purchases natural gas from twocompanies: Southern Gas and Northwest Gas.
Demand forecasts for the coming winter season are as follows:Hamilton County, 400 units; Butler County, 200 units; and ClermontCounty, 300 units. Contracts to provide the following quantitieshave been written: Southern Gas, 500 units; and Northwest Gas, 400units. Distribution costs for the counties vary, depending upon thelocation of the suppliers. The distribution costs per unit (inthousands of dollars) are as follows.
(a)
Develop a network representation of this problem. (Submit a filewith a maximum size of 1 MB.)
This answer has not been graded yet.
(b)
Develop a linear programming model that can be used to determinethe plan that will minimize total distribution costs.
Let
x11, x12, x13, x21, x22, x23 ≥ 0
(c)
Describe the distribution plan and show the total distributioncost.
(d)
Recent residential and industrial growth in Butler County hasthe potential for increasing demand by 100 units.
(i)
Create an updated distribution plan assuming Southern Gasbecomes the preferred supplier.
(ii)
Create an updated distribution plan assuming Northwest Gasbecomes the preferred supplier.
(iii)
Which supplier should Tri-County contract with to supply theadditional capacity?
The Tri-County contract should go to the supplier withthe ---Select--- highest lowest cost,i.e. ---Select--- Southern Gas NorthwestGas .