Hey guys I really need help with my assignment Your help wil

Hey guys. I really need help with my assignment. Your help will be so much appreciated. Thanks!!

A baseball team plays in a stadium that bolds 66000 spectators With the ticket price at $8 the average attendance has been 29000 When the puce dropped to $6 the average attendance rose to 33000 Assume that attendance is linearly related to ticket price. What ticket puce would maximize revenue?

Solution

Two points ( 29000 , $8) and ( 33000 , $6)

slope = ( 6 -8)/( 33000- 29000) = -2/4000 = -1/2000

y = -x/2000 + c ; 6 = -33000/2000 + c

c = 6 + 16.5 = 22.5

y = -x/2000 + 22.5 where x is no of spectators and y is price per ticket

Revenue , R(x) = x*y = x(-x/2000 + 22.5)

= -x^2/2000 + 22.5x

Maximum revenue : x = -b/2a = 22500 spectantors

max. R(x) = $ 253125