Question

The Valley High School student council is planning a dance. The school has 200 students. The lowest possible ticket price is $1.00, and they estimate that for every$0.50 increase in ticket price, 25 fewer students will attend. What ticket price will maximize the student council’s profit?

1. The maximum revenue is $312.50 for 125 students What number of students would attend at the lowest ticket price? At the lowest ticket price of$1.00 it is likely that all the 200 students would attend because it is the most affordable price
revenue for 200 students=$1.00*200 revenue for 200 students=$200.00
When ticket price increases to $1.50,there would reduction in attendance by 25 students, leaving only 175 students revenue for 175 students=$1.50*175
revenue for 175 students=$262.50 When the ticket price increases to$2.00 from $1.50, the attendance would reduce to 150 revenue for 150 students=$2.00*150
revenue for 150 students=$300.00 When the ticket price increases to$2.50, only 125 students would grace the event
revenue for 125 students=$2.50*125 revenue for 125 students=$312.50
When the ticket price increases to $3.00, only 100 students would be in attendance revenue for 100 students=$3.00*100
revenue for 100 students=$300.00 At this point, the revenue has started declining, hence, the maximum revenue is$312.50 for 125 students