Question

A coal-fired power plant can produce electricity at an operating cost of $0.06 per kilowatt-hour when running at its full capacity of 30 megawatts per hour, $0.16 per kilowatt-hour when running at 20 megawatts per hour, and $0.24 per kilowatt-hour when running at 10 megawatts per hour. A gas-fired power plant can produce electricity at a variable cost of $0.12 per kilowatt-hour at any capacity from 1 megawatt per hour to its full capacity of 5 megawatts per hour. The cost of constructing a coal-fired plant is $70 million, but it costs only $14 million to build a gas-fired plant.

Instructions: In part b, enter your answer as a whole number. In parts c and d, round your answers to 2 decimal places.

a. Consider a city that has a peak afternoon demand of 80 megawatts of electricity. If it wants all plants to operate at full capacity, what combination of coal-fired plants and gas-fired plants would minimize construction costs?

    

Sixteen gas-fired plants

One coal-fired plant plus ten gas-fired plants

Two coal-fired plants plus four gas-fired plants

b. How much will the city spend on building that combination of plants?

c. What will the average variable cost per kilowatt-hour be if you average over all 80 megawatts that are produced by that combination of plants? (Hint: A kilowatt is one thousand watts, while a megawatt is one million watts.)

d. What would the average variable cost per kilowatt-hour be if the city had instead built three coal-fired plants?

Answer 1

Ib part b we choose a whole number is $168million.
c) Based on the answer from a, we have 2 coal fired and 4 gas fired plants to operate at full capacity to fulfill 80 megawatts requirement.
Coal fired max capacity = 2*30 = 60 megawatts
Variable cost at max capacity for coal-fired = 0.06 $
Gas fired max capacity = 4*5 = 20 megawatts.
Variable cost at max capacity for gas-fired = 0.12 $
Average cost per kilowatt-hour = (0.05*60+0.12*20)/80 = 0.0675 $/kwh
d) 3 coal-fired plants -
2 plants at 30 MW capacity and 1 plant at 20 MW capacity
Average cost per kwh = (0.05*60+0.16*20)/80 = 0.0775 $/kwh