Question

A makeup company is producing new eyeliner pens. The cost for the new machinery needed is $450, and $2.50 for every pen produced. The company plans on selling the new eyeliner pens for $10 each. The inequality below was written to determine how many eyeliner pens the company would need to break even or make a profit. What is the minimum number of eyeliner pens the company must sell to break even or make a profit?

A. 90 eyeliner pens
B. 135 eyeliner pens
C. 155 eyeliner pens
D. 180 eyeliner pens

Answer 1

The minimum number of eyeliner pens the company must sell to break even or make a profit is 90 eyeliner pens.

Step-by-step explanation:

To break even or make a profit, the company must cover its costs, which include the cost of the machinery plus $2.50 for every pen produced. Let's assume the minimum number of eyeliner pens the company must sell is x. The cost equation can be represented as 450 + 2.5x. To find the minimum number of pens, we need to solve the inequality 450 + 2.5x ≤ 10x, which gives x ≥ ≈ 90. Therefore, the minimum number of eyeliner pens the company must sell to break even or make a profit is 90 eyeliner pens, so the correct option is A.