A baseball team plays in a stadium that holds 60,000 spectators. With the ticket

Question

A baseball team plays in a stadium that holds 60,000 spectators. With the ticket price at $10, the average attendance at recent games has been 27,000. A market survey indicates that for every dollar the ticket price is lowered, attendance increases by 3000.

a- Find a function that models the revenue in terms of ticket price. (Let x be the ticket price and R(x) be the revenue.)

b- Find the price that maximizes revenue from ticket sales.

c-What ticket price is so high that no revenue is generated?

Explanation / Answer

setting up the revenue function

a) R(x) = ( 27000 + 3000x ) ( 10 - x )

b) R(x) = - 3000x^2 + 3000 x + 270000

maximum revenue occurs at

x = - 3000 / 2 ( - 3000 )

x = 0.5

so, $ 0.5 maximizes revenue

c) setting R(x) = 0

- 3000x^2 + 3000 x + 270000 = 0

x = 10

so, at $ 10 , no revenue is generated

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