Word problem

Question

A student is working part time as a hairdresser. She can work no more than 24 hours a week. She charges $80 for a perm which takes 2 hours and charges $25 for a haircut which takes 30 minutes. How many perms and haircuts should she give to optimize revenue? What is the optimal revenue?

 

A) let x be the number of perms and y be the number of haircuts, write the object give function. 

 

B) list the contains

 

C) find the optimal revenue and how many cuts and perms the student must do to obtain it. 

Answer 1

The limiting factor is the number of hours per week, which is 24

 

So, if only perms are done, then $ = $80/perm x (24h ÷ 2h/p) = $80/h x 12h = $960

 

If only cuts are done, then $ = $25/c x (24h ÷ 0.5h/c) = $25/c x 48c = $1200

 

So, the student should do only cuts to make the maximum revenue.