SOLUTION: A company has determined that the profit, in dollars, it can expect from the manufacture and sale of x tennis racquets is given by: P= -0.01x2 + 168x - 120,000. How many racquets s

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Question 180243: A company has determined that the profit, in dollars, it can expect from the manufacture and sale of x tennis racquets is given by: P= -0.01x2 + 168x - 120,000. How many racquets should the company manufacture and sell to earn a profit of $518,000?
Answer by Mathtut(3670)   (Show Source): You can put this solution on YOUR website!
A company has determined that the profit, in dollars, it can expect from the manufacture and sale of x tennis racquets is given by: P= -0.01x2 + 168x - 120,000. How many racquets should the company manufacture and sell to earn a profit of $518,000
:
518000=-.01x^2+168x-120000
:

:
x=11000 and 5800
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=2704 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 11000, 5800. Here's your graph:
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