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Mathematics - Calculus - Integration in Commerce

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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).

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Solution Summary

The expert uses integration in commerce to determine how many years pass before the profitability of the machine begins to decline. The expert computes the net profit generated by the machine over its useful lifetime. A complete, neat and step-by-step solution is provided in the attached file.

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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) ...

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