Question

Revenue is given by R(q)=444q and cost is given by C(q)=10000+3q^2

a) At what quantity is profit maximized?
b) What is the profit at this production level?

Answer 1

Ah, I figured it out.

Profit = Revenue - Cost
P(q)=R(q)-C(q)
P(q)=444q - (10000 + 3q^2)
P(q) = 3q^2 + 444q -10000

a) P'(q) = 555-6q
444= -6q
|q|= 74

b) P(74) = -3(74)^2 + 444(74) - 10000
= $6425