1. An apartment complex has 150 two-bedroom units. The manager has determined that the monthly revenue for renting out x apartments can be estimated by the function R(x) = -0.1x3+ 10x? + 400x and that the monthly costs can be estimated by the function C(x) = 150x + 12,000. a) Write the profit P as a function of the number of apartment units rented out. b) Determine the marginal profit function. c) Compute the marginal profit when x = 50 and interpret your answer in context of the problem.

The price p (in dollars) and the demand x for a particular clock radio are related by the equation x = 5000 – 50p. (A) Express the price p in terms of the demand x, and find the domain of this function. (B) Find the revenue R(x) from the sale of x clock radios. What is the domain of R? (C) Find the marginal revenue at a production level of 2800 clock radios. (D) Interpret R'(3900) = – 56.00.

A piano manufacturer has a daily fixed cost of $1,700 and a marginal cost of $2,100 per piano. Find the cost C(x) of manufacturing x pianos in one day. C(x) = 2100 + 1700 X Use your function to answer the following questions. (a) On a given day, what is the cost of manufacturing three pianos? $8000 That's it! (b) What is the cost of manufacturing the third piano that day? $ 2100 Nicely done. (c) What is the cost of manufacturing the 11th piano that day? $ 2100 Excellent! (d) What is the variable cost? $ What is the fixed cost? $ What is the marginal cost? $ X per piano

3.) The revenue equation (in billions of dollars) for corn production in the United States is approximated by R(x)=0.016x² +1.034x+11.338 Where x is in billions of bushels. For example if you have 10 billion bushels, then x = 10. (Data from www.usda.gov) a.) Find the marginal revenue function b.) Find and interpret the marginal revenue for 15 billion bushels c.) Find and interpret the marginal revenue for 20 billion bushels