Let, price increased by x times.
New price = 40 + ( 1 × x ) = 40 + x
It is given that for each $1 increase park loses 300 visitors.
Number of visitors = ( 24000 - 300x )
So, revenue is given by :
R = ( 24000 - 300x )( 40 + x ) ....1)
To finding critical point :
R'(x) = 0
-300( 40 + x ) + ( 24000 - 300x ) = 0 .....By product law
-12000 - 300x + 24000 -300x = 0
600x = 12000
x = 20
So, revenue is maximum at x = 20 .
Putting x = 20 in equation 1) , we get :
R = ( 24000 - 300x )( 40 + x )
R = [ 24000 - 300(20)][40 + 20 ]
R = $1080000
Therefore, park should charge $( 40 + 20 ) = $60 for maximising the revenue and maximum revenue is $10,80,000 .
Hence, this is the required solution.
