Problem
The American Baker's Association reports that annual sales of bakery goods last year rose 15 percent, driven by a 50 percent increase in the demand for bran muffins. Most of the increase was attributed to a report that diets rich in bran help prevent certain types of cancer. You are the manager of a bakery that produces and packages gourmet bran muffins, and you currently sell bran muffins in packages of three. However, as a result of this new report, a typical consumer's inverse demand for your bran muffins is now P = 9 - 1.5Q.
If your cost of producing bran muffins is C(Q) = 3.0Q, determine the optimal number of bran muffins to sell in a single package and the optimal package price.