Word problem need help please

Question

A baseball team plays in a stadium that holds 55,000 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.
B) find the price that maximize revenue from ticket sales.
C) what ticket price is so high that no revenue is generated?

Answer 1

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

 

b)      10 - 1 = 9      10 - 0 = 10     30,000 x 9 = $270,000    270,000 x 10 = $270,000

 

c)      $19       (-3000 people for every dollar over $10;  9 x - 3000 = - 27000

 

 

 

Answer 2

Let x = number of $ that the price is decreased

 

R(x) = revenue  = (price per ticket)(number of tickets)

 

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

 

                            = -3000x² + 3000x  - 270000

 

Max revenue when x = -3000/[(2)(-3000)] = 0.5

That is, revenue is maximized if the ticket price is $9.50

 

R(x) = 0 if 10 - x = 0, so x = 10.  No revenue if the ticket price is $20.