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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
avatar+90995 
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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 !!!

 

 

cool cool cool

CPhill  Oct 29, 2018
edited by CPhill  Oct 29, 2018

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