300 room hotel in Macau is ﬁlled to full capacity every night at $800 per room. For each
additional $10 increase in rent, 3 fewer rooms are rented. If each rented room costs $160 to
service per day, how much should the hotel charge for each room to maximize proﬁt? Please help me, I got stuck in formulating these variables Thank You

Question

300 room hotel in Macau is ﬁlled to full capacity every night at $800 per room. For each
additional $10 increase in rent, 3 fewer rooms are rented. If each rented room costs $160 to
service per day, how much should the hotel charge for each room to maximize proﬁt?   Please help me, I got stuck in  formulating these variables Thank You

ganeshie8 · Answer

lets label the variables :
P : profit
x : number of rooms filled
w : rent of room

ganeshie8 · Answer

P =  wx - 160w ---------------- (1)

ganeshie8 · Answer

x = 300 - (w-800)/10 --------------------(2)

ganeshie8 · Answer

i think now u can substitute x in (1). and maximize P

ganeshie8 · Answer

lol typo in equation (2)
it must be :

x = 300 - 3(w-800)/10 --------------------(2)

anonymous · Answer

Thank You so much for your help

ganeshie8 · Answer

welcome.. :))

anonymous · Answer

sorry to disturb, but in equation 2 didn;t you mean p=wx-160x, thank you

ganeshie8 · Answer

yep... another typo lol. 
cost = 160 times num.of.rooms

nice catch :)

ganeshie8 · Answer

P =  wx - 160x ---------------- (1)
x = 300 - 3(w-800)/10 --------------------(2)

now both look correct to me..

anonymous · Answer

thx mate

ganeshie8 · Answer

yw :)