Proving employee hourly worth

Linear, quadratic, module, parametric equations

Proving employee hourly worth

Postby Guest » Fri Dec 21, 2018 7:40 pm

I’m looking to find a way to make an equation or line graph to show my employee my value and ahat they can afford to pay me without making things too complicated on their end.

Here’s how my pay works. I’m a mechanic who is paid flat rate (paid per job). I’m paid 26.52 an hour. Any time produced over 45 hours I get an extra .50c to my hourly rate, over 50 hours another .50c up until 65 hours where it maxes out at 2.50c total per hour added to my rate.

I do not know my cost of employment (overhead/ insurance and what not).

We charge 139.00 per hour to the customers.

Is there a way to make an equation to show the correlation between hours over 40 and the cost of my employment? Like how much more they profit off an employee who averages 60 hours a week.

I’m looking to adjust our pay plan and bonus levels to make it more fair for the technicians without over complicating things and blowing the managers minds. If there’s more info you need to help me out let me know

Thanks. I really appreciate it.

Re: Proving employee hourly worth

Postby Guest » Sat Mar 02, 2019 11:36 am

So an employee makes 25.52 dollars per hour for the first 45 hours, 26.02 for 45 to 50 hours, 26.52 for 50 to 65 hours, and 27.02 for anything more than 65 hours (per week I presume). That can be written as the "piecewise function", W(t):
W(t)= 25.52t for t< 45
W(t)= 1148.40+ 26.02(t- 45) for 45< t< 50 (the 1148.40 is for the first 45 hours)
W(t)= 1278.50+ 26.52(t- 50) for 50< t< 65 (the 1278.50 is for the first 50 hours)
W(t)= 1661.30+ 27.02(t- 65) for t> 65 (the 1661.30 is for the first 65 hours)
Multiplying the parentheses gives
W(t)= 25.52t for t< 45
W(t)= 26.02t- 22.42 for 45< t< 50
W(t)= 26.52t- 47.50 for 50< t< 65
W(t)= 27.02t- 95.00 for t> 65

Since t hours of work on a car brings in 139t dollars, the income, less employee wages is
W(t)= 113.48t for t< 45
W(t)= 112.98t- 22.42 for 45< t< 50
W(t)= 112.48t- 47.50 for 50< 5< 65
W(t)= 111.98t- 95.00 for t> 65.

However, be prepared for the management to point out that this does not include managers' salaries, cost of the building, health insurance and other perquistes given the employees, cost of supplies, etc.. It's not all profit!

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