Marginal Analysis of a Snow Blower

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Lesson Parent: 
Marginal Analysis as an Instantaneous Rate of Change
Problem: 

The cost and revenue functions for a snow blower are $C(n)=48n+19000$ and $R(n)=-0.25n^2+248n+2650$. Determine the marginal cost, revenue, and profit when producing and selling $250$ units.

Answer: 

The marginal cost, revenue, and profit are $\$48$, $\$123$, and $\$75$, respectively.

SAMPLE SOLUTION

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Solution: 

From the lesson associated with this problem we know that profit is given by

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From the lesson we also know that the marginal cost, marginal revenue, and marginal profit is given by $C'(n)$, $R'(n)$, and $P'(n)$, respectively. Each of these is a polynomial function and we know the derivative of a polynomial. Therefore,

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At $250$ units we have

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This means that we will increase our costs by $\$48<Sign in to see all the formulas>\$123$ and our profit by $\$75<Sign in to see all the formulas>251$ units.