Question
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.
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; and Clermont County, 300 units. Contracts to provide the following quantities have been written: Southern Gas, 500 units; and Northwest Gas, 400 units. Distribution costs for the counties vary, depending upon the location of the suppliers. The distribution costs per unit (in thousands of dollars) are as follows:
- Develop a linear programming model that can be used to determine the plan that will minimize total distribution costs. Let xij = amount shipped from supply node i to demand node j.
Min fill in the blank 2x11 + fill in the blank 3x12 + fill in the blank 4x13 + fill in the blank 5x21 + fill in the blank 6x22 + fill in the blank 7x23 s.t. fill in the blank 8x11 + fill in the blank 9x12 + fill in the blank 10x13 fill in the blank 11 fill in the blank 12x21 + fill in the blank 13x22 + fill in the blank 14x23 fill in the blank 15 fill in the blank 16x11 + fill in the blank 17x21 = fill in the blank 18 fill in the blank 19x12 + fill in the blank 20x22 = fill in the blank 21 fill in the blank 22x13 + fill in the blank 23x23 = fill in the blank 24 xij 0 for all i, j
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