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**+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 )

CPhill
Oct 5, 2018

#2**+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**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**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