Question

The owner of a skating rink rents the rink for parties at $1320 if 60 or fewer skaters attend, so that the cost per person is $22 if 60 attend. For each 5 skaters above 60, she reduces the price per skater by $0.50.

(a) Construct a table that gives the revenue generated if 60, 70, and 80 skaters attend. No. of skaters Price per Skater Total Revenue 60 $ 70 $ 80 $

(b) Does the owner's revenue from the rental of the rink increase or decrease as the number of skaters increases from 60 to 80? The revenue increases. The revenue decreases.

(c) Write the equation that describes the revenue for parties with x groups of five skaters more than 60 skaters. R(x) =

(d) Find the number of skaters that will maximize the revenue. skaters

Answer 1

a)

Price	No. of skaters	Total Revenue
22	60	$1320
21	70	$1470
20	80	$1600

b)As we can see from table, the revenue increases.

c) R(x)=Rate per skater * No of skaters

=(22-0.5x)(60+5x)   (as mentioned in question that x is the number of additional 5 skaters)

d) R'(x)=(-0.5)(60+5x)+(22-0.5x)(5)

=> -30-2.5x+110-2.5x=0

=> 5x=80

=> x=16

=> at x=16, we have a maxima

=>No of skaters = 60+5x=60+80=140