A manufacturer studies how the ratio of maintenance cost to production cost (in…

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

A manufacturer studies how the ratio of maintenance cost to production cost (in suitable monetary units) varies with the daily production level xx (in units). The ratio is modelled by R(x)=3x2+100x+4005x3−7x+200,x>0.R(x)=\frac{3x^{2}+100x+400}{5x^{3}-7x+200}, \quad x>0. (a) Calculate lim⁡x→∞R(x)\displaystyle \lim_{x\to\infty} R(x). (b) Interpret the value obtained in part (a) in the given context. State, in one short sentence, what the company can expect for very large production levels.

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