# The Valley High School student council is planning a dance. The school has 200 students. The lowest possible ticket price is \$1.00

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?

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1 week 2023-01-23T18:33:27+00:00 1 Answer 0 views 0

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
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