Q. 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 for every hour also 24 cents per kilowatt hour when running at 10 megawatts every 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.
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?