Given the following revenue and cost functions, find the maximum profit. (Recall that profit equals revenue minus cost.) R(x) = 73x - 2x; C(x) = 25x + 102

Question

Given the following revenue and cost functions, find the maximum profit. (Recall that profit equals revenue minus cost.)

R(x) = 73x - 2x; C(x) = 25x + 102

Answer 1

P(x)=R(x)-C(x)= 48x-2x^2-102

P'(x)=MR-MC=48-4x=0

x=48/4= 12= profit maximizing output

P(12)= 73(12)-2(12)^2 -120-25(12)

=24(12)-108

= 288-108=180 = max profit

if you try to treat the problem as written, without a squared term, then

P(x) = 46x-120 and

max profit = infinity