SOLUTION: Studies have shown that 400 people attend a high school basketball game when the admission price is $30 in the championship game, admission prices will increase for every $0.25 inc

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Question 1180633: Studies have shown that 400 people attend a high school basketball game when the admission price is $30 in the championship game, admission prices will increase for every $0.25 increase, 20 fewer people will attend. At what ticket will the revenue be maximized?
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
I think you mean 2 fewer people, not 20, because if the ticket sales are $30.25 and 380 people attend, one will be losing money, compared to 400 and $30.
Let x is number of $0.25 increase and multiples of 2 people.
(400-x)(($30+0.25x)
=12000-30x+100x-5x^2
the maximum is at x=-b/2a for this negative quadratic of -5x^2+70x+12000
this is x=70/10=7
so at $31.75 (7*$0.25-$1.75) and 386 people (400-7*2)
there is a maximum, or $12,255.50
graph%28300%2C300%2C-5%2C10%2C-500%2C14000%2C-5x%5E2%2B70x%2B12000%29