Question

A factory selling computers has a marginal cost function MC(x)=0.003x^2−3.372x+372 and a marginal revenue function given by MR(x)=372−3x, where x represents the number of computers. MC(x) and MR(x) are in dollars per unit. Find the total profit, or area between the graphs of these curves, between x=0 and the first intersection point of these curves with x>0. Enter your answer in dollars, rounded to two decimal places if needed.

Answer 1

marginal profit MP = MR-MC = 372−3x - (0.003x^2−3.372x+372)
MP = 0.372x - 0.003x^2
The graphs intersect at x = 124
so the profit is
P(x) = ∫[0,124] MP(x) dx