Question

a professional football team has a stadium which seats 60000. it is found that x tickets can be sold at a price of p=10-(x/10000) dollars per ticket. find the value of x and p at which the total money received will be a maximum.

Answer 1

thats a linear equation with a positive slope....

Answer 2

errr.. a negative slope lol;

Answer 3

p = -(1/100000) x + 10

Answer 4

when x = 0 you have a maximum of 10; the higher x goes, the less you make

Answer 5

or am i missing something

Answer 6

no

Answer 7

I don't think so. There's logic in your answer ^_^

Answer 8

this might be the derivative and is asking fo ryouto integrate from 0 to 60000

Answer 9

hmmm, no wait, wouldn't that be a minimum?

Answer 10

if 0 tickets are sold, then you gained p=10000

Answer 11

f'(x) = 0 at 10000/10 then

Answer 12

oh right lol, it's over (10,000) ^_^" my bad lol

Answer 13

f'(x)= 1000; integrate from 0 to 60000?

Answer 14

no need to integrate, from the function , you can figure out the maximum, just like you did :)

Answer 15

x increases= less money, like you've said. so the maximum is at x = 0?

Answer 16

well i am thinking that this is the derivative of a higher function; and its max value is at 1000 for x; so the integral would tell us the price right?

Answer 17

but wouldn't wouldn't the price be found after plugging in x =0 in the function? :)

Answer 18

if this was the true function then yes, but the wording has me believe that the optimazation is given by this equation; and not the true function...

Answer 19

mmm, so we have to optimize in this case? ^_^to find the maximum

Answer 20

i think so :) so we would integrate the given to find the true value; with x = 1000; becasue that is where p'(x) = 0

Answer 21

Alright, now I got what you mean lol

proceed ^_^

Answer 22

the 60000 gives us an initial condition; possiply at (0,60000)

Answer 23

so we'll integrate from 0->6000?

Answer 24

dunno if we integrate of simply anchor it in at (0,60000)

p=10-(x/10000)

Answer 25

P(x)=10x -x^2/2(10000) + C

Answer 26

10(1000) - (1000)(1000)/2(10000)

10000 - 500/10

Answer 27

10000 - 50 = 9950 +C

Answer 28

P(1000) = 60000 = 9950 + C

C = 60000 - 9950 = 50050

P(x) = 10(x) - x^2/20000 + 50050 ??

Answer 29

maybe integrate from 0 to 60000 :) ??? dunno

Answer 30

I think we have made it look more complicated than it seems, lol?

Answer 31

LOL!

Answer 32

do you know what I think?

Answer 33

broken question? lol

Answer 34

since the maximum price of tickets is achieved when x=0, then for 60000 seats, the maximum price will be = 600,000

Answer 35

.-. right?

Answer 36

maximum price = 600,000? or max revenue?

Answer 37

see the wording is off...

Answer 38

hmm, we have :\[p(x) = 10-\frac{x}{10000}\]

so

if we take x = 0:



\[p(0) = 10\]

so we can tell that the original price of the ticket is = 10.

Now for 60000 seats, we need 60000 people, so each person is going to buy a ticket. In the end, maximum price achieved = 600,000

I'm not sure, but I'm just computing what I have understood from the question ^_^" ahaha...

Answer 39

so the maximum values for x and p :

x = 0, and p = 10

Answer 40

i agree that that is a possible interpretation of the problem :) but maximum price is not 600,000; that would be revenue. Max price if anything would be 10 lol

Answer 41

oh, right >_< well, atleast you got what I mean =P

Answer 42

x=50,000
p=5
maximum money = p*x = 250,000

Answer 43

if x = tickets sold, then how can 0 ticket sold bring in 600,000 :)

Answer 44

where did you get the 50,000 and 5? .-.

Answer 45

money received is revenue which equals price*quantity
quantity is num seats sold = x
so the function to maximized is p*x = x(10-x/10,000)

Answer 46

annnnnnwaaaar~

lol ^_^

Answer 47

but the number of seats = 60,000 and not 50k lol :)

Answer 48

I don't know where you guys have reached. But, I think the idea here is to maximize the total money received.
Total money= price of one ticket * # of tickets= xp(x).

Answer 49

60,000 available not sold

Answer 50

so how did you get 50k?

Answer 51

i understand it now.... i think lol

Answer 52

differentiate above function
set =0
solve for x

Answer 53

p = 0 and solve for x?

Answer 54

whoever wrote this problem could have been clearer ;)

Answer 55

xp(x)=f(x)=10x-x^2/10,000
f'(x)=10-2x/10,000=0 implies x=50,000

Answer 56

oh well, clear or not, my brain is shutdown and doesn't want to study. I had calculus II at 8 and was playing in the whole time, and got out not understanding what on Earth I took today.

Answer 57

and I felt good abt it. I guess it's beacuse of the bananas I ate in the morning.

Answer 58

oh, I got you anwar, thank you ^_^

Answer 59

LOL!!

Answer 60

You're welcome. Am I right there?

Answer 61

it's TRUE! Bananas = get you excited, and I was off ~ completely OFF

Answer 62

hoenstly, I have no idea. My brain is unable to compute or accept any info atm.

Answer 63

but it looks right though ^_^

Answer 64

i was watching the cheerleaders and got distracted lol

Answer 65

LOL

Answer 66

HAHA.

Answer 67

waterlily do you get it? or do you need more help

Answer 68

my professor tried to grab my attention by trying, "TRYING" to introduce Taylor series today, but no hope, he gave up and ended the class after 1 hour =D!

Answer 69

I was like, I don't like taylor series, I want to learn Fourier series!

Answer 70

he was like, but it's not in the syllabus and etc etc etc

Answer 71

i get it thanks

Answer 72

loooooooooooong morning, it was HILARIOUS

Answer 73

oh, sorry waterlily ^_^" aha...

Answer 74

You have no more classes?

Answer 75

let's see, my ESPII professor, cancelled today's class at 10, so no class til 3:30 , hallalujah~!

Answer 76

and guess what!

Answer 77

what?!

Answer 78

I've got a test at that time! Heck knows what I'll during that hour. If I'm luney and off now, what will happen later on? ^_^

Answer 79

I think I and mr. "dumbcow" had the same answer. He was first though.

Answer 80

people usually revise, take advantage of these 4 free hours, but me? nooooooo, don't feel like it ._. I guess I need a day off.

Answer 81

lol.....LOL!

Answer 82

LOL

Answer 83

why did he call himself dumbcow?! :D

Answer 84

I find that a really funny and "creative" username :)

Answer 85

I have no idea.

Answer 86

cows are not dumb! they just don't get english that's all

Answer 87

Do you stay at university or go home during this 4 hours?

Answer 88

if cows are dumb for not understanding what we say, then we are dumb becase we don't understand what they say, right?

Answer 89

LOL. they don't get english heh? what about arabic?

Answer 90

I stay here, I don't want to get my mum tired.

Answer 91

neither

Answer 92

all they say is mooo

Answer 93

I don't agree with your "cow" theorem btw :P

Answer 94

with different wavelengths ~

Answer 95

But I like it :)

Answer 96

Hey, this is logic and I'm studying it this semester and I agree with my theorem

Answer 97

omg..I sound drunk LOL with bananas~

Answer 98

Nope, it's not.