2. A coal-fired power plant can produce electricity at a variable cost of 4 cents per kilowatt-hour when running at its full capacity of 30 megawatts per hour, 17 cents per kilowatt-hour when running at 20 megawatts per hour, and 24 cents per kilowatt-hour when running at 10 megawatts per hour. A gasfired power plant can produce electricity at a variable cost of 12 cents 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 $50 million but it only costs

$10 million to build a gas-fired plant. [LO19B.2]

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?

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

c. What will the average 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;

a megawatt is one million watts.)

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