math
posted by nhokaishiteru
miss Thao owns a small hotel with 30 identical rooms. she finds that if she charges a price of 12 dollars ( or less) per room per day, all the rooms are rented. for every 1 dollar in price, 2 rooms remain vacant. each day, maintenance cost 4 dollars per rented room and 1 for unrented room. what price should miss thao charge n order to maximize her daily profit? hint: profit = revenue  costs
Help me, thanks a lots

Reiny
current number of rooms = 30
current price per room = 12
let the number of additional increases of $1 be n
numbers of rooms rented = 30  2n
number of rooms not rented = 30  (302n) = 2n
price per room = 12 + n
Profit = (12+n)(302n)  4(30n)  1(2n)
= 360 + 6n 2n^2  120 + 4n  2n
= 2n^2 + 8n + 240
by Calculus:
d(profit)/dn = 4n + 8
= 0 for a max of profit
4n = 8
n = 2
the price per room should be 12+n = 12+2
= $ 14.00
if you don't know calculus:
profit = 2n^2 + 8n + 240
the n of the vertex = 8/4 = 2
so the price should be $ 14.0 
nhokaishiteru
tks Reiny so much :x
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