Answer to Question #8571 in Calculus for Jo

Question

A company must purchase at least 500 credits but no more than2000 credits, at a cost of $800 per credit. The company finds that when it purchases between 500 and 1000 carbon credits, it earns $1200 in revenue per credit. However, its per-credit revenue is reduced by 20 cents for each credit purchased in excess of 1000 credits

a) Define the profit function P(x) as revenue minus costs (measured in dollars), where x is the number of carbon credits purchased.
Show that P(x) =400x 500 < x < 1000 (lines under <)
600x - 0.2x^2 1000 < x < 2000 (line under second <)
b) Are there any values of x with 500 < x < 2000 for which the derivative P'(x) is not defined? If so, state what these values are.