The American Baker’s Association reports that annual sales of bakery goods last

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) = .5Q, determine the optimal number of bran muffins to sell in a single package and the optimal package price.

Optimal Package size: ___5_____ units

Optimal Package price: $ ________

I already found the package size to be 5 units however what is the price?

I found the

Explanation / Answer

Set P = MC to obtain 8 - 1.5Q = 0.5 and solve to obtain the optimal package size, Q = 5 units.

The total value to a consumer of a package of 5 muffins is $28.75

computed as:-

(.5)($8 – $0.5)(7) + ($0.5)(5) =$28.75

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