The American Baker’s Association reports that annual sales of bakery goods last
ID: 1131441 • Letter: T
Question
The American Baker’s Association reports that annual sales of bakery goods last year rose 15%, driven by a 50% 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 a 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.
Optimal package size: units
Optimal package price: $
Explanation / Answer
Solution :- Marginal cost (MC) = 0.50 (First derivative of total cost function).
Equating Price (P) and Marginal cost (MC) in the given question,
8 - 1.50 Q = 0.50
8 - 0.50 = 1.50 Q
7.50 = 1.50 Q
Q = 7.50 / 1.50
Q = 5.
Optimal Package size (Q) = 5.
Optimal Package price (P) = 0.50 * 5 * (8 - 0.50) + 0.50 * 5
= 0.50 * 5 * 7.50 + 2.50
= 18.75 + 2.50
= $ 21.25
Conclusion :-
Optimal Package size 5 units. Optimal Package price $ 21.25 (approx).Related Questions
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