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

Tri-County Utilities, Inc.
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 Northwest Gas. Demand forecasts for the coming winter season are as follows:
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 per unit (in thousands of dollars) are as follows:
From To
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 (in thousands of dollars).
Let
x11 = amount shipped from Southern Gas to Hamilton
x12 = amount shipped from Southern Gas to Butler
x13 = amount shipped from Southern Gas to Clermont
x21 = amount shipped from Northwest Gas to Hamilton
x22 = amount shipped from Northwest Gas to Butler
x23 = amount shipped from Northwest Gas to Clermont
(d)
Recent residential and industrial growth in Butler County has the potential for increasing demand by 100 units.
(i)
Create an updated distribution plan assuming Southern Gas becomes the preferred supplier.
(ii)
Create an updated distribution plan assuming Northwest Gas becomes the preferred supplier.
(iii)
Which supplier should Tri-County contract with to supply the additional capacity?
The Tri-County contract should go to the supplier with the