The American Baker’s Association reports that annual sales of bakery goods last
ID: 1118123 • Letter: T
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 = 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.
a. optimal package size: _______
b. optimal package price: _______
Explanation / Answer
Set P = MC
& obtain 8 - 1.5Q = 2
Q = 6/1.5 = 4 units.
a. optimal package size: 4 units
The totalvalue to a consumer of a package of 4 muffins is $20 (computed as (.5)($8 – $2)(4) + (2)(4) =$20).
b. optimal package price: $20
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