+0  
 
+1
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5
avatar+105 

A company that sells widgets has to pay $500 in maintenance fees each day and then it pays each worker $8 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?

mathbum  Oct 5, 2018
 #1
avatar+92890 
+1

Total costs  =  500 +  8 * 8x   = 

 Fixed cost + (hrs per day)( hourly wage rate) (x)  =

  500 + 64x      where x is the number of workers we need

 

Total Revenue  = 

(hrs per day) (number of widgets/hour)(sales price/widget) (x)  =

8 * 5 * 3.10 * x  =  124x

 

And we want to solve this

 

124x >  500 + 64x      subtract  64x from both sides

 

60x > 500

 

x > 500/60

 

x > 8.33  workers

 

So...we need 9 workers (at a minimum )

 

 

 

cool cool cool

CPhill  Oct 5, 2018
 #3
avatar+105 
0

I got 8.33/9 as well having the same work, but it is wrong? Do you see anything wrong with your work?

mathbum  Oct 6, 2018
 #2
avatar+14579 
+2

500 = fixed cost

n 8 x 8 = labor cost

n x 5 x3.1 x 8 = money brought in from sales

 

500 + n 8x8  = n x 5 x 3.1 x 8

            500 + 64n = 124 n

             500 = 60n

               n = 8.33          ~~  9 employees  

ElectricPavlov  Oct 5, 2018
 #4
avatar+105 
0

I got 8.33/9 as well having the same work, but it is wrong? Do you see anything wrong with your work?

mathbum  Oct 6, 2018
 #5
avatar+14579 
0

It would change if the COST of producing the Widgets were included....but that info was not given in the question......Was it to be included but omitted?

ElectricPavlov  Oct 7, 2018

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