# solution

The state of Missouri has three major power-generating companies identified as 1, 2, and 3. During the months of peak demand, the Missouri Power Authority authorizes these companies to pool their excess capacity and to produce and distribute electricity to smaller independent power utilities that do not have generators large enough to handle all the demand. The supply, up to the excess capacity, is distributed on the basis of cost per kilowatt-hour transmitted.

The table below contains the costs (in cents, Â¢) per kilowatt-hour (kwh) of transmitting power from the major companies 1, 2, and 3 to each of four different small independent companies W, X, Y, and Z. Also shown in the table are the demand and capacity for power in millions of kilowatt-hours (Mkwh).

TO

 FROM W X Y Z Excess Capacity (Mkwh) 1 12Â¢ 4Â¢ 9Â¢ 5Â¢ 45 2 2Â¢ 1Â¢ 4Â¢ 7Â¢ 50 3 8Â¢ 12Â¢ 6Â¢ 6Â¢ 55 Unfilled Demand (Mkwh) 40 20 50 20

The problem is to determine the best way to allocate the power, in millions of kilowatt-hours, from the major companies to the small independents so as to keep the total distribution costs to the lowest that is possible.

(NOTE: Unit distribution costs entered in the body of the table above are listed in units of cents/kwh. Capacity and demand entered in the â€œrim cellsâ€ are both in units of Mkwh. HINT: In your modeling, convert the units costs to \$/Mkwh.)

Define all the decision variables. Be explicit and specific (including units).

state the objective function in terms of the decision variables and the constraints of the situation described in terms of the decision variables.

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