Question 159109
The question states "Maximizing Revenue- A large hotel is considering the following group discount on room rates. The regular price for a room is $120, but for each room rented the price decreases by $2 per room. ie. one room costs 118, 2 rooms cost $116 X 2=232 and so on.
a)What is the maximum revenue?
b) What is the number of rooms that should be rented? 
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Let r = number of rooms rented at the group discount
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Revenue = n(120 - 2n)
Revenue = 120n - 2n^2
Revenue = -2n^2 + 120n
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Because the 'a' coefficient of the equation is negative, we KNOW that the parabola opens downward (upside down U).
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To find the vertex, rearrange the equation into the "vertex form":
y= a(x-h)^2+k
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Basically, we're manipulating our equation into the "vertex form":
Revenue = -2n^2 + 120n
Revenue = -2(n^2 - 120n)
Completing the square:
Revenue = -2(n^2 - 60n - 900) + 1800
Revenue = -2(n^2 - 30)^2 + 1800
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Now, we know that (h,k) is at (30, 1800)
This vertex represents the peak of the parabola -- answering your questions:
a)What is the maximum revenue? $1800
b) What is the number of rooms that should be rented? 30