Answer:
Ticket price 11,5 $
R(max) = 132750 $
Step-by-step explanation:INCOMPLETE QUESTION
The ticket price is missing
We will assume 12 $
Let call x the decreasing number of the ticket price
The revenue is
R = ticket price * numbers of spectator
R(x) = ( 12 - x ) * ( 11000 + 1000*x ) for all 0 ≤ x ≤ 4 ( the seating capacity is 15000 )
R(x) = 132000 + 12000*x - 11000*x - 1000*x²
R(x) = 132000 + 1000*x - 1000*x²
Taking derivatives on both sides of the equatio we get:
R´(x) = 1000 - 2000x
R´(x) = 0 ⇒ 1000 - 2000x = 0
x = 1000/2000 ⇒ x = 0,5 $
We notice that R´´(x) < 0 then we have a maximum for x = 0,5
and the price is 12 - 0,5 = 11,5 $ for ticket
and the R(max) is
R(max) = 132000 + 1000*0,5 + 1000* (0,5)²
R(max) = 132000 + 500 + 250
R(max) = 132750 $
