A toy manufacturer's cost for producing q units of a game is given by

Question

C(q) = 1480 + 3.8q + 0.0006q2. If the demand for the game is given by
p = 8.6 − 1/440q
how many games should be produced to maximize profit? (Round your answer to the nearest integer.)

Answer 1

revenue = price * demand
profit = revenue - cost
Hmmm. no indication of the selling price, unless that's p. If so, then revenue
r(q) = q*p(q) - c(q) = q(8.6-1/440 q) - (1480 + 3.8q + 0.0006q^2)
= -0.00287q^2 + 3.8q - 1480
For maximum revenue, now just find the vertex of the parabola. (where dr/dq = 0)