The owner of a skating rink rents the rink for parties at $240 if 20 or fewer skaters attend, so that the cost per person is $12 if 20 attend. For each 5 skaters above 20, she reduces the price per skater by $0.50. (a) Construct a table that gives the revenue generated if 20, 30, and 40 skaters attend. No. of skaters Price per Total Revenue Skater 20 30 40 $ $ (b) Does the owner's revenue from the rental of the rink increase or decrease as the number of skaters increases from 20 to 40? The revenue increases. The revenue decreases. (c) Write the equation that describes the revenue for parties with x groups of five skaters more than 20 skaters. R(x) = (d) Find the number of skaters that will maximize the revenue. skaters (e) Find the maximum revenue. $ (f) When the revenue is at the maximum possible, what price is paid per skater?
The owner of a skating rink rents the rink for parties at $240 if 20 or fewer skaters attend, so that the cost per person is $12 if 20 attend. For each 5 skaters above 20, she reduces the price per skater by $0.50. (a) Construct a table that gives the revenue generated if 20, 30, and 40 skaters attend. No. of skaters Price per Total Revenue Skater 20 30 40 $ $ (b) Does the owner's revenue from the rental of the rink increase or decrease as the number of skaters increases from 20 to 40? The revenue increases. The revenue decreases. (c) Write the equation that describes the revenue for parties with x groups of five skaters more than 20 skaters. R(x) = (d) Find the number of skaters that will maximize the revenue. skaters (e) Find the maximum revenue. $ (f) When the revenue is at the maximum possible, what price is paid per skater?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The owner of a skating rink rents the rink for parties at $240 if 20 or fewer skaters attend, so that the cost per person is $12 if 20 attend. For each 5 skaters above 20, she reduces the price per skater by $0.50.
(a) Construct a table that gives the revenue generated if 20, 30, and 40 skaters attend.
No. of skaters
Total Revenue
20
30
40
Price per
Skater
=
(b) Does the owner's revenue from the rental of the rink increase or decrease as the number of skaters increases from 20 to 40?
O The revenue increases.
O The revenue decreases.
$
$
$
(c) Write the equation that describes the revenue for parties with x groups of five skaters more than 20 skaters.
R(x):
(d) Find the number of skaters that will maximize the revenue.
skaters
(e) Find the maximum revenue.
$
(f) When the revenue is at the maximum possible, what price is paid per skater?
$
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