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 = 8 - 1.5Q. 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. Instruction: Enter your response for the optimal package price rounded to two decimal places. Optimal package size: units Optimal package price: $

1. The the optimal number of bran muffins to sell in a single package is 4 units.

2. The optimal package price is $2.

Explanation:

Under the theory of production in Economics, optimal quantity is obtained when price (P) is equal to the marginal cost (MC) (i.e. when P = MC).

From the question, we have:

P = 8 - 1.5Q (1)

C(Q) = 2.0Q (2)

To obtain MC, C(Q) in equation (2) is differentiated with respect to Q as follows:

MC = C'(Q) = 2 (3)

We will equate equate (1) and (3) to have:

P = MC

8 - 1.5Q = 2

Rearrange and solve for Q:

1.5Q = 8 - 2

1.5Q = 6

Q = 6 ÷ 1.5

Q = 4.0

Therefore, the optimal number of bran muffins to sell in a single package is 4 units.

Substitute Q = 4 into equation (1), we have:

P = 8 - (1.5 × 4) = 8 - 6 = 2.0

Therefore, the optimal package price is $2.0.

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