Swift Cuts makes $12 on each manicure and $18 on each haircut. A manicure takes 30min and a haircut take 50min and there are 5 stylists who each work 6hrs a day. If the salon can schedule 50 appointments a day, how many should be manicures and hose many haircuts in order to maximize profit? What is the maximum profit?

The equations i got was:

let x be manicure
let y be haircut

P = 12x + 18y

30x+50y ≤ 50
50y ≤ 1800 (minutes)
x ≥ 0
y ≥ 0

are my equations correct? If not, please explain? This is just a question I opted to study. So in no way are you helping me cheat. ;

Question

Swift Cuts makes $12 on each manicure and $18 on each haircut. A manicure takes 30min and a haircut take 50min and there are 5 stylists who each work 6hrs a day. If the salon can schedule 50 appointments a day, how many should be manicures and hose many haircuts in order to maximize profit? What is the maximum profit? 

The equations i got was: 

let x be manicure 
let y be haircut 

P = 12x + 18y 

30x+50y ≤ 50 
50y ≤ 1800 (minutes) 
x ≥ 0 
y ≥ 0 

are my equations correct? If not, please explain? This is just a question I opted to study. So in no way are you helping me cheat. ;

dumbcow · Answer

you almost got it
$$x+y \le 50$$
$$30x+50y \le 1800$$

dumbcow · Answer

btw is your user pic of Mr Bean ?
if so, i think hes hilarious

anonymous · Answer

ahh thank you. :) I think so too! good memories from childhood.