Find the total profit, the maximum value of the total profit, and the value of x at which it occurs when the revenue is given by R(x)=240x-x^2 and the cost is given by C(x)=5000+8x

Question

The total profit, P(x)=-x^2+_______x-5000

Answer 1

p = r - c

= 240 x - x^2 - 5000 - 8 x

= - x^2 + 232 x - 5000

Answer 2

x^2 - 232 x = -p - 5000

x^2 - 232 x + 13456 = -p - 5000 + 13456
(x - 116)^2 = -(p - 8456)
vertex at
profit = 8456
and
x = 116