Question

A baseball team plays in the stadium that holds 68000 spectators. With the ticket price at 9 the average attendance has been 28000. When the price dropped to 7, the average attendance rose to 34000.

a) Find the demand function p(x), where x is the number of the spectators. (assume p(x) is linear) p(x)= (-2/5000)x+18.3333333

b) How should be set a ticket price to maximize revenue? <<<<<<

Answer 1

they give you 2 data points to construct a line with

(9,28000)
(7,34000)

Answer 2

subtract the points to find your slope:

(9,28000)
-(7,34000)
-----------
-2,-6000; slope = y/x = 6000/2 = 3000

now calibrate the line equation with one of the points to get:

p(x) = 3000x -3000(9) + 28000

p(x) = 3000x + 1000

Answer 3

my -2 is wrong :) 9-7 = 2 ; so the slope is gonna be -3000

Answer 4

p(x) = -3000x +3000(9) + 28000

p(x) = -3000x +55000 maybe?

Answer 5

I have my p(x) though. It's the second part which I don't quite understand how to get using my p(x)

Answer 6

I think it is just P(x)* x which will give us parabola

Answer 7

revenue = r(x) = number of people attending * price per ticket

r(x) = p(x)*x

r(x) = (-3000x +55000)x

r(x) = -3000x^2 +55000x; take derivative or find vertex

Answer 8

r(x) = -3x^2 + 55 ; for simplicity

Answer 9

dropped an x :)

r(x) = -3x^2 + 55x;

r'(x) = -6x + 55; r(x)=0 when x=55/6

Answer 10

1000* 9.1666666.......

9166.6666.... maybe?

Answer 11

9.16 lol forget the 1000

Answer 12

9.17 works better in the r(x) equation

Answer 13

!!! I've been trying to get an answer for that for the past 2 days. Thanks, amistre :]