Assume that a pharmaceutical company has a monopoly over the production of master cream, a drug used on skin rashes. Further suppose that the demand for master cream is given by the expression QD = 1,500 - P, where QD is the quantity demanded (in bottles) and P is the price. Assume that the company's costs are given by the expression
TC = 100 - Q^2 + 5Q^3.
a) What is the profit-maximizing level of output of master cream (in bottles)?
b) What is the profit-maximizing price?
c) What is the maximum level of profit?