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, 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. 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, while 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?
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, 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. 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, while 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?
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