Question

A baseball team plays in he stadium that holds 72000 spectators. With the ticket price at 9 dollars, the average attendence has been 30000. When the price dropped to 7 dollars, the average attendence rose to 36000.
a) Find the demand function p(x), where x is the number of the spectators. (assume that p(x) is linear)
p(x)=
b) What should be the ticket price so that the revenue is maximized?

Answer 1

i got p(x) to be (-x/300)+129 and its not correct...any suggestions?

Answer 2

If p(x) is linear and two points that satisfy this is (30000,9) and (36000,7), then we have:
\[p(x)=\frac{9-7}{30000-36000}(x-30000)+9 \\
\Rightarrow p(x)=-\frac{1}{3000}(x-30,000)+9\\
\Rightarrow p(x)=-\frac{x}{3000}+19\]
If we let R(x):=revenue function, then
\[R(x)=xp(x)=-\frac{x^2}{3000}+19x\]
Can you find the x where this is maximum and the corresponding p(x)?

Answer 3

how would i do this?

Answer 4

Take the derivative wrt x and set to zero.

Answer 5

ok so then x= 28500

Answer 6

Yep.

Answer 7

but thats incorrect according to my hw

Answer 8

And when x=28500, p(x)=???

Answer 9

Your answer book is asking for p(x). :)

Answer 10

And when x=28500, p(x)=2707519

Answer 11

NOOOO

Answer 12

-28500/3000 + 19 = ?

Answer 13

@GT 29.4

Answer 14

You calculated R(x) above to get 2707519?

Answer 15

-28500/3000 + 19 = -9.5 + 19 = $9.5

Answer 16

ok thanks

Answer 17

Remember, in that equation for p(x), the value 19 signifies where attendance drops to ZERO. So, no price above $19 even makes sense.

Answer 18

ok i got it thanks

Answer 19

The manager of a large apartment complex knows from experience that 80 units will be occupied if the rent is 320 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 8 dollar increase in rent. Similarly, one additional unit will be occupied for each 8 dollar decrease in rent. What rent should the manager charge to maximize revenue?

Answer 20

Good!

Answer 21

how abt this?

Answer 22

Post it separately. It is the policy of this site.

Answer 23

o ok

Answer 24

http://openstudy.com/study?signup#/updates/4f937854e4b000ae9eca13ca