Find the Marginal Profit

Primary tabs

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

The cost and revenue functions for a product are $R(n)=-0.004n^2+11.5n-5375$ and $C(n)=0.014n+13.75$. What is the marginal profit for 750 units?

Answer: 

$\$5.49$ per unit.

SAMPLE SOLUTION

All of our problems have fully worked out, logical solutions. We connect every solution to its underlying lesson so you can understand the concepts needed to solve any problem and reinforce your learning by practicing with similar problems. All of the formulas are available to our subscribers, but here is a sample of the problem solution you will see when you log in:



Solution: 

The profit is given by

<Sign in to see all the formulas>

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,

<Sign in to see all the formulas>


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