The American Baker\'s Association reports that annual sales of bakery goods last
ID: 1126571 • 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 :1 0.5Q If your cost of producing bran muffins is CQ)-7.5Q, 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: $Explanation / Answer
Optimal output is that level of output corresponding to which MR equals MC.
Demand function -
P = 11 - 0.5Q
TR = P * Q = (11 - 0.5Q) * Q = 11Q - 0.5Q2
MR = dTR/dQ = d(11Q - 0.5Q2)/dQ = 11 - Q
Cost function
C = 7.5Q
MC = dC/dQ = d(7.5Q)/dQ = 7.5
Equating MR and MC
11 - Q = 7.5
Q = 3.5
P = 11 - 0.5Q = 11 - (0.5*3.5) = 11 - 1.75 = 9.25
Thus,
Optimal package size = 3.5 units
Optimal package price = $9.25
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