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 = -0.01x^2 + 168x - 120,000 How m

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> 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 = -0.01x^2 + 168x - 120,000 How m      Log On


   

Question 50535This question is from textbook Applied College Algebra
: 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 = -0.01x^2 + 168x - 120,000
How many racquets should the company manufacture and sell to earn a profit of $518,000? This question is from textbook Applied College Algebra

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x, where P = -0.01x^2 + 168x - 120,000, and P=580,000.

518000 = -.01x^2 + 168x - 120000

Subtract 518000 from each side, and solve the quadratic equation:
0=-0.01x^2 + 168x -638000

This can be solved with a graphing calculator, by graphing
y =-0.01x^2 +168x - 638000, and finding the x-intercept(s), where y = 0.

This is a parabola that opens downward, and the vertex at x=%28-b%29%2F%282a%29+
x=%28-168%29%2F%28-0.02%29=8400, at which point y = 67600
I plotted the graph with a graphing calculator using a window of x from 0 to 12,000, and y from 0 to 100,000.
The x-intercepts are at x=5800 and at x=11000, and those are the numbers of raquets that can be sold to end up with $518,000 profit.
graph+%28800%2C400%2C+0%2C12000%2C+0%2C100000%2C+-0.01x%5E2+%2B168x+-+638000%29+


Hey, it would have been easier to use a pluggable solver to solve the quadratic equation 0=-0.01x^2 + 168x -638000!!

The final answer is x=5800 and at x=11000.

R^2