Cost Minimization

Carolina Power and Light (CP&L) is a small electric utility located in the Southeast. CP&L currently uses coal-fired capacity to satisfy its base load electricity demand, which is the minimum level of electricity demanded 24 hours per day, 365 days per year.

CP&L currently burns both high-sulfur eastern coal and low-sulfur western coal. Each type of coal has its advantages. Eastern coal is more expensive ($50 per ton) but has higher heat- generating capabilities. Although western coal does not generate as much heat as eastern coal, western coal is less expensive ($25 per ton) and does not cause as much sulfur dioxide pollution. CP&L's base load requirements are such that at least 2,400 million BTUs must be generated per hour. Each ton of eastern coal burned generates 40 million BTUs, and each ton of western coal burned generates 30 million BTUs. To limit sulfur dioxide emissions, the state's Environmental Protection Agency (EPA) requires CP&L to limit its total burning of sulfur to no more than 1.5 tons per hour. This affects CP&L's coal usage, because eastern coal contains 2.5% sulfur and west- ern coal contains 1.5% sulfur. The EPA also limits CP&L particulate emissions to no more than 900 pounds per hour. CP&L emits 10 pounds of particulates per ton of eastern coal burned and 15 pounds of particulates per ton of western coal burned.

A. Set up and interpret the linear program that CP&L would use to minimize hourly coal usage costs in light of its constraints.

B. Calculate and interpret all relevant solution values.

C. Holding all else equal, how much would the price of western coal have to rise before only eastern coal would be used? Explain.