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SOLUTION: Maximizing Revenue: A large hotel is condidering giving the following froup discount on room rates: the regular price of $120 decreases by $2 for each room rented. For example, one
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Question 274917
:
Maximizing Revenue: A large hotel is condidering giving the following froup discount on room rates: the regular price of $120 decreases by $2 for each room rented. For example, one room costs $118, two rooms cost $116 x 2=$232, three rooms cost $114 x 3=$342 and so on. a)Write a formula for a function R that gives the revenue for renting x rooms. b)Sketch a graph of R. What is a reasonable domain? c)Determine the maximum revenue and the corresponding number of rooms rented.
Answer by
ankor@dixie-net.com(18980)
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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
:
b)Sketch a graph of R.
A graph of this equation
:
What is a reasonable domain?
easy to see it would be from 1 to 60 rooms (x)
:
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 =
x = +30 rooms rented would give max revenue
:
Find the vertex
y = -2(30^2) + 120(30)
y = -2(900) + 3600
y = -1800 + 3600
y = $1800 max revenue:
:
:
Confirm this
room cost: 120-2(30) = 60; then 30 * 60 = $1800