Question 1153135
Tickets to a school dance cost $4 and the projected attendance is 300 people.
 For every $1 increase in the ticket price, the dance committee projects that attendance will decrease by 5 attendees.
 Determine the dance committee’s greatest possible revenue. What ticket price will produce the greatest revenue?
:
Let x = no. of $1 increases and no. of 5 less attendees
Revenue = ticket price * no. of attendees
R(x) = (4 + x) * (300 - 5x)
FOIL
R(x) = 1200 - 20x + 300x - 5x^2
a quadratic equation
R(x) = -5x^2 + 280x + 1200
Max rev occurs on the line of symmetry, using x = -b/(2a)
x = {{{(-280)/(2*-5)}}}
x = 28 ea $1 increases will give max revenue
That would be: 4 + 28 = $32 a ticket
:
No. attending the dance: 300 - (5*28) = 160 attendees
:
Max revenue: 32 * 160 = $5120 vs only $1200 at original price