Suppose you are the marketing manager for Fruit of the Loom.An individual's inverse demand for Fruit of the Loom women's underwear is estimated to be P = 25 − 3Q (in cents).If the cost to Fruit of the Loom to produce an item of women's underwear is C(Q)= 1 + 4Q (in cents),compute the price Fruit of the Loom should charge for a package of women's underwear.
A) $1.09
B) $1.02
C) $108.50
D) $136.50

Question

Quizplus · Accepted Answer

To find the optimal price, we need to set marginal revenue (MR) equal to marginal cost (MC), and solve for Q. Then, we can plug Q back into the demand function to find the optimal price (P).

MR = dTR/dQ = d(P*Q)/dQ = P + Q*dP/dQ
MC = dTC/dQ = 4

Setting MR = MC:
25 - 3Q + Q*(-3) = 4
22 = 6Q
Q = 3.67

Plugging Q back into the demand function:
P = 25 - 3(3.67) = $11.99

However, the unit of the demand function is in cents, so the actual price would be $0.1199. Therefore, the optimal price for a package of women's underwear is $1.02, which is answer B.

Suppose You Are the Marketing Manager for Fruit of the Loom.An