Question

for the cost and price functions below, find a) the number, q, of units that produces maximum profit; b) the price, p, per unit that produces maximum profit; and c) the maximum profit, p.
c(q) = 80 + 16q; p = 60 - 2q

a) the number, q, of units that produces maximum profit is q = 11.
b) the price, p, per unit that produces maximum profit is p = $\square.

Explanation:

Step1: Identify the price function

The price function is given as \( p = 60 - 2q \).

Step2: Substitute q = 11 into the price function

We know from part (a) that the quantity \( q \) that maximizes profit is 11. Substitute \( q = 11 \) into the price function:
\( p = 60 - 2(11) \)

Step3: Calculate the price

First, calculate \( 2(11) = 22 \). Then, subtract this from 60: \( 60 - 22 = 38 \).

Answer:

38