Find the Marginal Profit

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

The cost and revenue functions for a product are R(n)=−0.004n2+11.5n−5375 and C(n)=0.014n+13.75. What is the marginal profit for 750 units?

Answer: 

$5.49 per unit.

SAMPLE SOLUTION

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Solution: 

The profit is given by

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The marginal profit is P′(n). We know that P(n) is a polynomial and that the derivative of a polynomial is easily determined. Therefore,

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At 750 units we have <Sign in to see all the formulas>. So at 750 units our marginal profit is $\$5.49<Sign in to see all the formulas>$5.486to$5.49$ because we don't have fractions of a penny.)