A coal-based power plant consumes 500 tons of coal per hour to produce 700 MW of electricity.

Question:

A coal-based power plant consumes 500 tons of coal per hour to produce 700 MW of electricity. Sixty percent of the heat content in the coal is lost as heat. The coal contains 20 percent ash. The fuel value of coal is 30,000 kJ/kg. By selling the electricity, the power plant earns a profit of $2 x 10^-4per kilowatt-hour. The ash is temporarily stored behind large dams. The power plant is looking for alternative ways of disposing of the ash. Landfilling costs $10-6 per kilogram but prices are expected to increase by 4 percent per annum. Another option is to sell the ash to a local cement manufacturer. This option will involve transportation of the ash to the cement plant, which will cost $7.5 x 10-6 per kilogram.

(a) When will it be profitable for the power plant to start transporting the ash to the cement plant?

(b) By using ash, the cement plant will replace minerals that it buys for $10-5 per kilogram. Each kilogram of mineral is equivalent to 1.4 kg of ash. If landfilling remains almost free, how much should the cement manufacturer pay the power plant so that both have no net additional cost?