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)=−0.25n2+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>$123andourprofitby$75<Sign in to see all the formulas>251$ units.