A coal-fired power plant can produce electricity at avariable cost of $0.04 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 $60 million, but it costs only $12 million to build a gas-fired plant.

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?

multiple choice

• 2 coal-fired plants and 4 gas-fired plants
• 16 gas-fired plants
• 1 coal-fired plant and 10 gas-fired plants

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

$ million

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

$ per kilowatt-hour

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

$ per kilowatt-hour