Marginal Analysis of Air Conditioner Units

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

A company produces highly specialized air conditioning units for the meat packing industry. The cost to produce $n$ units is $C(n)=0.07n+1100$ and the revenue gained in selling those $n$ units is $R(n)=-0.025n^2+2n+2400$. Determine the marginal cost, marginal revenue, and marginal profit when producing 32 units.

Answer: 

$C'(32)=0.07$, $R'(32)=0.40$, and $P'(32)=0.33$

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 32 units we have

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This means that we will increase our revenues by only <Sign in to see all the formulas> and our profit by <Sign in to see all the formulas> when we increase our production to 33 units.