Question

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+184x-120,000 How many racquets should the company manufacture and sell to earn a profit of $658,800?

Answer 1

To determine the quantity of tennis racquets to produce for a profit of $658,800, we set the profit equation equal to the desired profit and solve for x. The resulting quadratic equation is then solved using an appropriate method to find the optimal number of tennis racquets.

Step-by-step explanation:

To find out how many tennis racquets the company should manufacture and sell to earn a profit of $658,800, we need to set the profit equation equal to $658,800 and solve for x.

Profit equation: P = -0.01x² + 184x - 120,000

Set the profit to $658,800:

-0.01x² + 184x - 120,000 = 658,800

First, move $658,800 to the left side of the equation:

-0.01x² + 184x - 120,000 - 658,800 = 0

This simplifies to:

-0.01x² + 184x - 778,800 = 0

We can now solve this quadratic equation for x by either factoring, using the quadratic formula, or by numerical methods such as graphing or using a calculator.