A company has determined that the profit P , in dollars, it can expect from the manufacture and sale of x tennis racquets is given by . How many racquets should the company manufacture and sell to earn a profit of $425,000?

Question

A company has determined that the profit P , in dollars, it can expect from the manufacture and sale of x tennis racquets is given by  . How many racquets should the company manufacture and sell to earn a profit of $425,000?

Quizplus · Accepted Answer

We want to solve for x in the equation P = 11x - 0.003x^2 = 425,000.

Rearranging, we get:

0.003x^2 - 11x + 425,000 = 0

Using the quadratic formula:

x = (-(-11) ± sqrt((-11)^2 - 4(0.003)(425,000))) / (2(0.003))

x ≈ 5,000 or x ≈ 8,400

Therefore, the company should manufacture and sell either 5,000 or 8,400 tennis racquets to earn a profit of $425,000. So, the answer is choice C.

A Company Has Determined That the Profit P , in Dollars