Assignment:
Profit over the useful life of a machine -
Suppose that when it is t years old, a particular industrial machine generates revenue at the rate
R'(t) = 6,025 - 8t^2 dollars per year and that operating and servicing costs accumulate at the rate
C'(t) = 4,681 + 13t^2 dollars per year.
a) How many years pass before the profitability of the machine begins to decline?
b) Compute the net profit generated by the machine over its useful lifetime.
c) Sketch the revenue rate curve y = R'(t) and the cost rate curve y = C'(t) and shade the region whose area represents the net profit computed in part (b).
Provide complete and step by step solution for the question and show calculations and use formulas.