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Question 909068: Pretensions Spa makes $10 on each pedicure and $17 on each foot massage. A pedicure takes 25 minutes, a massage takes 75 minutes, and there are 10 employees who each work 6 hours per day. The spa can schedule 60 appointments per day. How many appointments in one day should be pedicures in order to maximize profit? What is the maximum profit?
Answer by JulietG(1812)   (Show Source):
You can put this solution on YOUR website! There are a possible 60 work hours per day.
Since a pedicure makes $24/hr and the massage makes $13.6/hr, you'll want to maximize the pedicures.
How many pedicures can be done in a six hour period (we're assuming that only one employee works at a time on a person)?
6 hours * 60 minutes = 360 / 25 = 14.4 -- you can't use the .4. We'll have to see later if it's worth it to maximize the time.
14 pedicure appointments * all 10 employees = 140 pedicure appointments @ $10 = $1400.
If one of those appointments per person is a massage, then we have:
1 massage appointment (360-75=285 mins left) @$17 = 17, plus
(285/25=11.4) 11 pedicure appointments @$10 = $110. $127 per employee = $1270.
If two of those appointments per person is a massage, then we have:
2 massage appointments (360-150=210 mins left) @17 = $34, plus
(210/25=8.4) 8 pedicure appointments @$10 = $80. $114 per employee = $1140
3 massage appointments (360-225=135 mins left) @$17 = $51, plus
(135/25=5.4) 5 pedicure appointments @$10 = $50. $101 per employee = $1010
4 massage appointments (360-300=50 mins left) @$17 = $68, plus
(50/25 = 2) 2 pedicure appointments @$10 = $20. $88 per employee = $880
As the number of pedicure appointments decline, even accounting for unused employee time, the revenue also declines.
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