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Permit Costs
A natural gas peaker plant sells electricity to a local utility at a price of $100 per MWh, with a fixed cost of $100,000 and variable costs 50q + 0.0005q2. (q is measured in MWh).
Question 1: What is the profit maximizing quantity of power to sell and how much profit will the generator make?
Question 2: Burning fossil fuel, the plant produces a lot of carbon dioxide. A new environmental regulation requires that for every Mcf of natural gas burned, an emission permit for 0.5 tons of CO2 must be purchased. It takes approximately 7.4 Mcf of natural gas to generate 1 MWh of electricity, and the cost of a 1ton CO2 permit is $12. Rewrite the cost function from 5a to include the cost of the permit and solve for the profit maximizing quantity of power and profit.
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