Expert: Abe Mantell - 5/23/2009

Question
Hi! I need help calculating this problem. It's a 3 part question:
-I have an average wage of $6.45/hr and use 985 hours per week. If I keep my labour target at 7%, what are my weekly sales?
-If I increase my average wage to $7.50/hr, and still use 985 hours/wk, based on what my sales were in the 1st question, what is my new labour %?
-If I need to reduce my labour % back down to 7%, with the same sales, how many man hours would I need to reduce down to, in order to maintain a wage of $7.50/hr?
I hope you can help me. I'm lost!
Sara:)

Answer
Hello Sarah,

- I gather that you mean the labor wages must be 7% of sales, yes?
..if so, then let x=the total sales/week.  The total labor wages
..are $6.45*985 = $6353.25 ... now we want 7% of x = 6353.25
..thus, 0.07x=6353.25 ==> x=6353.25/0.07 = 90760.7143
..So, the sales should be $90,760.71 per week.
- $7.50*985 = $7387.50...which is 7387.50/90760.25 = 0.0814 = 8.14%
- For 7% labor, you can only spend $6353.25, so let x=# of man-hours.
..$7.50x=$6353.25 ==>x=6353.25/7.50=847.1 hrs.  Thus, you need to
..reduce the hours by 985-847.1 or 137.9 hrs or rounded to 138 hrs.

OK?  I hope this helps!

Abe