The owner of a skating rink rents the rink for parties at $360 if 30 or fewer sk

Question

The owner of a skating rink rents the rink for parties at $360 if 30 or fewer skaters attend, so that the cost per person is $12 if 30 attend. For each 5 skaters above 30, she reduces the price per skater by $0.50. (a) Construct a table that gives the revenue generated if 30, 40, and 50 skaters attend No. of skatersPrice per Total Revenue Skater 30 40 50 (b) Does the owner's revenue from the rental of the rink increase or decrease as the number of skaters increases from 30 to 50? The revenue increases. O The revenue decreases. (c) Write the equation that describes the revenue for parties with x more than 30 skaters. R(x) (d) Find the number of skaters that will maximize the revenue. skaters

Explanation / Answer

a) if 30 attended = 30*12 = $360

if 40 attended = 40*11 = $440

if 50 attended = 50*10 = $500

b) revenue from the rental of the rink increase as the number of skaters increases from 30 to 50

c) R(x) = (12-0.5x)(30+5x)  

d) when sketers are 80 there will be maximum profit

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