Assignment:
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.
Provide complete and step by step solution for the question and show calculations and use formulas.