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Chapter 3: Q. 87 (page 157)

Suppose that the manufacturer of a

gas clothes dryer has found that, when the unit price is p dollars, the revenue R (in dollars) isR(p)=-4p2+4000p

What unit price should be established for the dryer to maximize revenue? What is the maximum revenue?

Short Answer

Expert verified

The unit price should be $500 and the maximum revenue is R(x)=1000000

Step by step solution

01

Given information

We are given a equationR(p)=-4p2+4000p

02

Find the vertex

The coefficient of the square term is negative hence the parabola opens downwards hence the maximum value is at the vertex

The vertex can be given as

x=-b2ax=40008x=500

Hence the price of each unit should be

$500

03

To find the revenue

substitute 500 for p in the equation

R(p)=-45002+4000500R(p)=-100000+200000R(p)=1000000

The revenue is $1000000

04

Conclusion

The price of a single unit is $500

And the total revenue is $1000000

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