Question

Select the correct answer from the drop-down menu.

A company sells its products to distributors and boxes of 10 units each. it's profits can be modeled by this equation, where p is the profit after selling n boxes.

p = -n² + 300n + 100,000

Use this equation to complete the statement.

The company breaks even, meaning the profits are only $0, when it sells _____ boxes.

Options for Blank:

A: 200 or 500

B: 500

C: 150

D: 200​

Answer 1

B. 500

Explanation:

Given the profit made by a company modeled by the function

p = -n² + 300n + 100,000

The company breaks even when p = 0

To get the number of boxes sold when the company breaks even, we will substitute p = 0 into the equation.

0 = -n² + 300n + 100,000

multiply through by -1

0 = n² - 300n - 100,000

n² - 300n - 100,000 = 0

(n² - 500n) + (200n - 100,000) = 0

n(n-500)+200(n-500) = 0

(n+200)(n-500) = 0

n+200 = 0 and n-500 = 0

n = -200 and n = 500

Since n cannot be negative

Hence n = 500

This means that the company breaks even when it sells 500 boxes