The state of Missouri has three major power-generating companies identified as 1

Question

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

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 costs in the table above are listed in units of cents/kwh. Capacity and demand are both in units of Mkwh. HINT: In your modeling, convert the unit costs to either cents/Mkwh or $/Mkwh.)

Please just convert these units to $/Mkwh

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

Explanation / Answer

First we need to identify the lowest transmission rates for each small company

For W its 1 cent if transmitted through 3...demand 40, supply 50

For X its 1 cent if transmitted through 2...demand 20, supply 55

For Y its 4 cents if transmitted through 3...demand 50, supply 50

For Z its 5 cents if transmitted through 1...demand 20, supply 45

There is a conflict for supply at lowest price in W & Y. For W the second lowest power supply is through 2 but it increases the cost by 7 cents, whereas for Y incremental cost is 2 cents if moved to 2

So the alloaction would be as below to keep the transmission costs at minimum

For W entire 40 Mkwh from 3

For X entire 20 Mkwh from 2

For Z entire 20 Mkwh from 1

For Y entire 10 Mkwh from 3, 35 Mkwh from 2 & 5 Mkwh from 1

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