Question 274917
 A large hotel is considering giving the following group discount on room rates:
 the regular price of $120 decreases by $2 for each room rented.
:
 a)Write a formula for a function R that gives the revenue for renting x rooms.
x = no. of rooms
Rev = no. of room * price of each room
R(x) = x(120 - 2x)
R(x) = -2x^2 + 120x
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b)Sketch a graph of R.
A graph of this equation
{{{ graph( 300, 200, -20, 80, -500, 2500, -2x^2+120x) }}} 
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What is a reasonable domain?
easy to see it would be from 1 to 60 rooms (x)
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 c)Determine the maximum revenue and the corresponding number of rooms rented.
You see this from the graph, but we can find it using the axis of symmetry and vertex
y = -2x^2 + 120x; where a= -2; b = 120
x = {{{(-120)/(2*-2)}}}
x = +30 rooms rented would give max revenue
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Find the vertex
y = -2(30^2) + 120(30)
y = -2(900) + 3600
y = -1800 + 3600
y = $1800 max revenue: 
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:
Confirm this
room cost: 120-2(30) = 60; then 30 * 60 = $1800