Question

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 = 10 - 2Q. If your cost of producing bran muffins is C(Q) = 2.0Q, determine the optimal number of bran muffins to sell in a single package and the optimal package price.

Answer 1

The optimal number of muffins to sell in a single package can be determined by equation marginal revenue to marginal cost.

Here,

TR: P*Q = 10Q- 2Q²

MR= 10 -4Q

TC= 2Q

MC=2

Thus, MR=MC

10-4Q=2

Q* = 2

P* = 6