Abaseball team plays in a stadium that holds 52000 spectators. with the ticket price at $9 the average attendance has been 21000. when the price dropped to $6, the average attendance rose to 26000.
a) find the demand function p(x), where x is the number of the spectators. (assume p(x) is linear.)
b) how should ticket prices be set to maximize revenue?

a) p(x)=-0.0006x +21.6

b) $10.80

Step-by-step explanation:

a) Assuming that p(x) is linear, the slope can be found by:

Applying the point (21000; $9) to the general linear equation gives us the demand function:

b) Revenue is given by the number of tickets sold multiplied by the price, the revenue function is:

The value of x for which the revenue function's derivate is zero is the number of spectators that yield the maximum revenue:

At x = 18,000, tickets price are:

it's equivalent, so we can say that its equal.

let's call the denominator x and the numerador is 18 less then denominator, x - 18.

multiply

2.x = 5.(x - 18)

2x = 5x - 90

90 = 5x - 2x

90 = 3x

x = 90/3

x = 30

so: