Question

Studies have shown that 400 people attend a high school basketball game when the admission price is

$3.00. In the championship game, admission prices will increase. For every $0.25 increase, 20 fewer
people will attend. At what ticket price will the revenue be maximized?

Answer 1

Explanation:

A $320 ticket price will the revenue be maximized

Answer 2

Let x=number of $0.25 increases, so the equation for revenue=price*number of tickets or people) becomes

Revenue=($3.00+$0.25x)(400-20x)

where ($3.00+$0.25x) :increase in price

and

(400-10x) : decrease in number of people

Expanding Revenue

Revenue[R]=1200-60x+100x-5x²:1200+40x-5x²

Taking the derivative of R and set it equal to 0:

R'=0+40-10x=40-10x

we have

R'=0

40-10x=0

x=40/10

x=4

So the ticket price is $3.00+$0.25*4=$4

The number of people will attend is 400-20*4=$320

At $320 ticket price will the revenue be maximized.