A company that sells widgets has to pay $500 in maintenance fees each day and then it pays each worker $15 per hour. Each worker makes 5 widgets per hour, which are sold at $3.10 each. What is the least number of workers the company has to hire in order to make a profit in an 8-hour workday?

I got 126 workers minimum, but I believe it should be smaller. Any thoughts?

mathbum
Oct 29, 2018

#1**+2 **

Let W be the number of workers [ per day ] that we need to make a profit

Total costs = 500 + 15 * 8 * W (1)

Total Revenue = 5 ( 3.10) * 8 * W (2)

We want to solve this for W

(2) > (1)

5 ( 3.10) * 8 * W > 500 + 15 * 8 * W simplify

124W > 500 + 120W subtract 120 W from both sides

4W > 500 divide both sides by 4

W > 125

So...you are correct....we need 126 workers [ at a minimum ] to make a profit !!!

CPhill
Oct 29, 2018