Question

A baseball team plays in he stadium that holds 48000 spectators. With the ticket price at 8 dollars, the average attendence has been 19000. When the price dropped to 6 dollars, the average attendence rose to 24000.
a) Find the demand function p(x), where p(x) is the number of the spectators. (assume that p(x) is linear)

b) What should be the ticket price so that the revenue is maximized?

Answer 1

The problem says: "Assume that p(x) is linear"
where p(x) is the number of spectators and x is the ticket price.

So we can assume p(x) = mx + b

You are given two points: when x = $8, p(x) = 19,000
and when x = $6, p(x) = 24,000

Solve for m and b and you will have the demand function p(x)

Answer 2

okay I got it! @ranga

Answer 3

8-(1/2500)(x-19000)

Answer 4

now how would I get b?

Answer 5

@ranga ??

Answer 6

I am replying to two other questions. So I will stop by in between.

p(x) = mx + b
x = $8, p(x) = 19,000
19000 = m(8) + b
x = $6, p(x) = 24,000
24000 = m(6) + b

Two equations, two unknowns:
8m + b = 19000 ---- (1)
6m + b = 24000 ----- (2)

Subtract (2) from (1). That will get rid of b. Solve for m.
Then put that m in (2) and solve for b.

Answer 7

@ranga are you still there?

Answer 8

Well i got part a already. how would i do part b?

Answer 9

What is the p(x) you got?

For part b)
Revenue R(x) = x * p(x)

To maximize revenue, find the first derivative and equate it to 0 and solve for x.

Answer 10

8-(1/2500)(x-19000)

Answer 11

I get p(x) = -2500x + 39000

I can verify it is correct because if I put x = 8, I get p(8) = 19000
if I put x = 6, I get p(6) = 24000
which agree with the data given in the problem.