How do you solve this problem? I’m stuck?
Hotel Prices
Doug asked:
You manage a 180 unit motel. All units will be occupied, on average, when you charge $50 per day per unit. Experience shows that for each $1 per day per unit that you increase the price, you will accrue 2 vacancies. Each occupied room costs $4 per day to clean and supply. On this basis, what price, in dollars, should you charge per unit per day to maximize your profit?
Bessie
You manage a 180 unit motel. All units will be occupied, on average, when you charge $50 per day per unit. Experience shows that for each $1 per day per unit that you increase the price, you will accrue 2 vacancies. Each occupied room costs $4 per day to clean and supply. On this basis, what price, in dollars, should you charge per unit per day to maximize your profit?
Bessie
July 30th, 2009 at 2:15 pm
Joann
Let’s say n=the number of additional dollars charged.
The money you’ll make on a given day is:
m=(50+n-4)(180-2n)=(n+46)(-2n+180)=-2n^2+88n+8280.
Take the derivative and find a zero:
m’=-4n+88, n=22
Take the second derivative to ensure that it’s a local maximum:
m”=-4; negative indicates local max
Therefore, 50+22=72 is the optimal room rate.
July 31st, 2009 at 9:23 am
Jack
Let’s say that we charge $x more than $50.
Then occure 2x vacancies,so we have
180-2x units occupied,hence the profit is
P(x)=(180-2x)*(50+x)-
(180-2x)*4
P(x)=(180-2x)*(46+x)
P(x)=-2x^2+88x+8280
P’(x)=-4x+88
P’(x)=0–>x=22
Because P”(x)=-4
August 1st, 2009 at 4:22 am
Tracy
simple equation of attitude- dress casual….