Thread: Solving rational inequalties application problem help

1. 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 $\displaystyle R(x)=-x^2+10x$ and $\displaystyle C(x)=4x+5$, 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 :

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

Is this the right inequality to solve the problem?

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

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