A baseball team plays in a stadium that holds 56,000 spectators. With the ticket

Question

A baseball team plays in a stadium that holds 56,000 spectators. With the ticket price at $10, the average attendance at recent games has been 24,000. A market survey indicates that for every dollar the ticket price is lowered, attendance increases by 3000. Find a function that models the revenue in terms of ticket price. (Let x represent the price of a ticket and R represent the revenue.) Find the price that maximizes revenue from ticket sales. What ticket price is so high that no revenue is generated?

Explanation / Answer

Lets find demand function ( price , attendance ) = ( 10 , 24000)

another point : ( 9 , 27000)

slope = -3000

y = -3000x + 54000

Revenue : R(x) = x*y = -3000x^2 + 54000x

Price that maximises revenue is given by vertex :

x = -54000/2*-3000 = $9

No revenue : R(x) = 0

-3000x^2 + 54000x =0

x( -3000x + 54000) =0

x = 54000/3000 = $18

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