The waste hauling company profits are stated as the difference between revenue and costs. That is P(x) = R(x) - C(x), where x is the number of tons processed. Find the maximum profit and the number of tonnage which must be processed in order to yield the maximum profit for each of the following:
a) R(x) = 5x; C(x) = 0.0001x2 + 1.2x + 60.
b) R(x) = 50x - 0.5x2; C(x) = 10x + 3.
c) R(x) = 20x - 0.1x2; C(x) = 4x +2.
(a) P(x) = 5x - 0.0001x^2 - 1.2x - 60 = 3.8x - 0.0001x^2 - 60
dP(x)/dx = 3.8 - 0.0002x = 0
Therefore, x = 19,000
At x = ...
Solve show the equations and simplify.