A coal-fired power plant can produce electricity at a variable cost of 5 cents per kilowatt-hour when running at its full capacity of 30 megawatts per hour, 16 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 gas-fired 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 costs only $10 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.

1. 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

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

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

$ ____million

1. What will be the averagecost 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

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

$ _____per kilowatt-hour