Solving rational inequalties application problem help

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April 7th 2011, 03:50 PM
Devi09

Solving rational inequalties application problem help

Here's the problem:

An economist for a sporting goods company estimates the revenue and cost functions for the production of a new snowboard. These functions are $R(x)=-x^2+10x$ and $C(x)=4x+5$ , respectively, where x is the number of snowboards produced, in thousands. The average profit is defined by the function AP(x) = P(x) / x , where P(x) is the profit function. Determine the production levels that make AP(x) > 0

What i did is :

$-x^2+1x + 4x+5 > 0$

Is this the right inequality to solve the problem?
April 7th 2011, 04:14 PM
pickslides

Won't profit be $\displaystyle P(x) = R(x)-C(x) = -x^2+10x-(4x+5) = -x^2+6x-5$ ?
April 7th 2011, 04:37 PM
Devi09

Quote:

Originally Posted by pickslides

Won't profit be $\displaystyle P(x) = R(x)-C(x) = -x^2+10x-(4x+5) = -x^2+6x-5$ ?

Yeh, so i factored out the negative and put the equation into the quadratic formula to find the x's which are 6.74 and -0.74. So -0.74 < x < 6.74

but the answer according to the book is 1 < x < 5