Question

A company uses the function P(x)=-2x²+500x-3050 to estimate the total profi for producing and selling x units of its product. How many units must the company produce to earn a profit of at least $25,000 ?

Answer 1

To find the number of units the company must produce to earn a profit of at least $25,000, we need to set up a quadratic inequality and solve for the range of values of x.

Step-by-step explanation:

To find the number of units the company must produce to earn a profit of at least $25,000, we can set up the inequality:

-2x² + 500x - 3050 ≥ 25000

Next, we can rearrange the inequality to set it equal to zero:

-2x² + 500x - 3050 - 25000 ≥ 0

This quadratic inequality can then be solved using various methods such as factoring, graphing, or the quadratic formula. The solutions will give us the range of values for x, representing the number of units the company must produce to earn a profit of at least $25,000.