anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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amistre64
  • amistre64
thats a linear equation with a positive slope....
amistre64
  • amistre64
errr.. a negative slope lol;
amistre64
  • amistre64
p = -(1/100000) x + 10

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More answers

amistre64
  • amistre64
when x = 0 you have a maximum of 10; the higher x goes, the less you make
amistre64
  • amistre64
or am i missing something
anonymous
  • anonymous
no
anonymous
  • anonymous
I don't think so. There's logic in your answer ^_^
amistre64
  • amistre64
this might be the derivative and is asking fo ryouto integrate from 0 to 60000
anonymous
  • anonymous
hmmm, no wait, wouldn't that be a minimum?
anonymous
  • anonymous
if 0 tickets are sold, then you gained p=10000
amistre64
  • amistre64
f'(x) = 0 at 10000/10 then
anonymous
  • anonymous
oh right lol, it's over (10,000) ^_^" my bad lol
amistre64
  • amistre64
f'(x)= 1000; integrate from 0 to 60000?
anonymous
  • anonymous
no need to integrate, from the function , you can figure out the maximum, just like you did :)
anonymous
  • anonymous
x increases= less money, like you've said. so the maximum is at x = 0?
amistre64
  • amistre64
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?
anonymous
  • anonymous
but wouldn't wouldn't the price be found after plugging in x =0 in the function? :)
amistre64
  • amistre64
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...
anonymous
  • anonymous
mmm, so we have to optimize in this case? ^_^to find the maximum
amistre64
  • amistre64
i think so :) so we would integrate the given to find the true value; with x = 1000; becasue that is where p'(x) = 0
anonymous
  • anonymous
Alright, now I got what you mean lol proceed ^_^
amistre64
  • amistre64
the 60000 gives us an initial condition; possiply at (0,60000)
anonymous
  • anonymous
so we'll integrate from 0->6000?
amistre64
  • amistre64
dunno if we integrate of simply anchor it in at (0,60000) p=10-(x/10000)
amistre64
  • amistre64
P(x)=10x -x^2/2(10000) + C
amistre64
  • amistre64
10(1000) - (1000)(1000)/2(10000) 10000 - 500/10
amistre64
  • amistre64
10000 - 50 = 9950 +C
amistre64
  • amistre64
P(1000) = 60000 = 9950 + C C = 60000 - 9950 = 50050 P(x) = 10(x) - x^2/20000 + 50050 ??
amistre64
  • amistre64
maybe integrate from 0 to 60000 :) ??? dunno
anonymous
  • anonymous
I think we have made it look more complicated than it seems, lol?
anonymous
  • anonymous
LOL!
anonymous
  • anonymous
do you know what I think?
amistre64
  • amistre64
broken question? lol
anonymous
  • anonymous
since the maximum price of tickets is achieved when x=0, then for 60000 seats, the maximum price will be = 600,000
anonymous
  • anonymous
.-. right?
amistre64
  • amistre64
maximum price = 600,000? or max revenue?
amistre64
  • amistre64
see the wording is off...
anonymous
  • anonymous
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...
anonymous
  • anonymous
so the maximum values for x and p : x = 0, and p = 10
amistre64
  • amistre64
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
anonymous
  • anonymous
oh, right >_< well, atleast you got what I mean =P
dumbcow
  • dumbcow
x=50,000 p=5 maximum money = p*x = 250,000
amistre64
  • amistre64
if x = tickets sold, then how can 0 ticket sold bring in 600,000 :)
anonymous
  • anonymous
where did you get the 50,000 and 5? .-.
dumbcow
  • dumbcow
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)
anonymous
  • anonymous
annnnnnwaaaar~ lol ^_^
anonymous
  • anonymous
but the number of seats = 60,000 and not 50k lol :)
anonymous
  • anonymous
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).
dumbcow
  • dumbcow
60,000 available not sold
anonymous
  • anonymous
so how did you get 50k?
amistre64
  • amistre64
i understand it now.... i think lol
dumbcow
  • dumbcow
differentiate above function set =0 solve for x
anonymous
  • anonymous
p = 0 and solve for x?
amistre64
  • amistre64
whoever wrote this problem could have been clearer ;)
anonymous
  • anonymous
xp(x)=f(x)=10x-x^2/10,000 f'(x)=10-2x/10,000=0 implies x=50,000
anonymous
  • anonymous
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.
anonymous
  • anonymous
and I felt good abt it. I guess it's beacuse of the bananas I ate in the morning.
anonymous
  • anonymous
oh, I got you anwar, thank you ^_^
anonymous
  • anonymous
LOL!!
anonymous
  • anonymous
You're welcome. Am I right there?
anonymous
  • anonymous
it's TRUE! Bananas = get you excited, and I was off ~ completely OFF
anonymous
  • anonymous
hoenstly, I have no idea. My brain is unable to compute or accept any info atm.
anonymous
  • anonymous
but it looks right though ^_^
amistre64
  • amistre64
i was watching the cheerleaders and got distracted lol
anonymous
  • anonymous
LOL
anonymous
  • anonymous
HAHA.
dumbcow
  • dumbcow
waterlily do you get it? or do you need more help
anonymous
  • anonymous
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!
anonymous
  • anonymous
I was like, I don't like taylor series, I want to learn Fourier series!
anonymous
  • anonymous
he was like, but it's not in the syllabus and etc etc etc
anonymous
  • anonymous
i get it thanks
anonymous
  • anonymous
loooooooooooong morning, it was HILARIOUS
anonymous
  • anonymous
oh, sorry waterlily ^_^" aha...
anonymous
  • anonymous
You have no more classes?
anonymous
  • anonymous
let's see, my ESPII professor, cancelled today's class at 10, so no class til 3:30 , hallalujah~!
anonymous
  • anonymous
and guess what!
anonymous
  • anonymous
what?!
anonymous
  • anonymous
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? ^_^
anonymous
  • anonymous
I think I and mr. "dumbcow" had the same answer. He was first though.
anonymous
  • anonymous
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.
anonymous
  • anonymous
lol.....LOL!
anonymous
  • anonymous
LOL
anonymous
  • anonymous
why did he call himself dumbcow?! :D
anonymous
  • anonymous
I find that a really funny and "creative" username :)
anonymous
  • anonymous
I have no idea.
anonymous
  • anonymous
cows are not dumb! they just don't get english that's all
anonymous
  • anonymous
Do you stay at university or go home during this 4 hours?
anonymous
  • anonymous
if cows are dumb for not understanding what we say, then we are dumb becase we don't understand what they say, right?
anonymous
  • anonymous
LOL. they don't get english heh? what about arabic?
anonymous
  • anonymous
I stay here, I don't want to get my mum tired.
anonymous
  • anonymous
neither
anonymous
  • anonymous
all they say is mooo
anonymous
  • anonymous
I don't agree with your "cow" theorem btw :P
anonymous
  • anonymous
with different wavelengths ~
anonymous
  • anonymous
But I like it :)
anonymous
  • anonymous
Hey, this is logic and I'm studying it this semester and I agree with my theorem
anonymous
  • anonymous
omg..I sound drunk LOL with bananas~
anonymous
  • anonymous
Nope, it's not.
anonymous
  • anonymous
wait what?o_o
anonymous
  • anonymous
yes it is
anonymous
  • anonymous
let me read it again.
anonymous
  • anonymous
how can bananas get you drunk?
anonymous
  • anonymous
lol. Yes, your theorem makes sense :P
anonymous
  • anonymous
there's this chemical compound in it, called tyro something something that get's you super duper powerful well, it usually gets ppl calm, but I don't know why it's the opposite effect on me? ._.
anonymous
  • anonymous
see, I told you so , I told you so, I told you so~
anonymous
  • anonymous
omg...please, bare with me this time and you'll never see me talk like this again >_<, I apologize guys
anonymous
  • anonymous
never eat bananas in the morning = lesson of today
anonymous
  • anonymous
You didn't say anything wrong!!
anonymous
  • anonymous
I sound DRUNK LOL
anonymous
  • anonymous
I don't eat bananas at all
anonymous
  • anonymous
I don't know how "drunk people" sound. So, I don't knwo if you do sound like one :)
anonymous
  • anonymous
know*
anonymous
  • anonymous
I love bananas and my professor recommened us to eat a banana every morning to calm the nerves, but it's not WORKING with me, it's not CALMING my nevers, it's getting me OFF~
anonymous
  • anonymous
lol
anonymous
  • anonymous
I'm just having one of my childish moments right now ^_^"
anonymous
  • anonymous
o_o...
anonymous
  • anonymous
lol?
anonymous
  • anonymous
These are the best moments. Enjoy them as much as you can
anonymous
  • anonymous
and you + mr"dumbcow" are getting a medal for soling the questionariO~
anonymous
  • anonymous
sigh~ I just need a break
anonymous
  • anonymous
I didn't get a weekend for 2 weeks now, and I need one
anonymous
  • anonymous
:(
anonymous
  • anonymous
busy busy, quizzes, tests, quizzes, tests, studies, da da da ~
anonymous
  • anonymous
Have a day off yo!!
anonymous
  • anonymous
but you know what?
anonymous
  • anonymous
exactly, that's what I was thinking. I'm going to my professor now, my lab professor and I'll tell him to excuse me from tomorrow's class. I just have one lab class tomorrow morning. I'll skip it, ofcourse after telling him that, and have FUN
anonymous
  • anonymous
that's it, one day off is all I need
anonymous
  • anonymous
YAAY.. I love "off" days!!
anonymous
  • anonymous
The one you make by yourself are the best <3
anonymous
  • anonymous
I don't lol. If I don't do something or work, I go NUTS, but for the first time, I AM HAPPY ABOUT IT! LOL
anonymous
  • anonymous
I KNOW!
anonymous
  • anonymous
I want to do something crazy !
anonymous
  • anonymous
I'll mis-match my clothes
anonymous
  • anonymous
for a start LOL
anonymous
  • anonymous
LOL.. Day off does not mean you just sleep all day long. It is just "freedom". You "DO" whatever you like
anonymous
  • anonymous
I don't sleep LOL! with this energy I can't! I don't even sleep during afternoons, I go play outside, paint, smash something, read, solve, ....no solving lol ummmmmmm
anonymous
  • anonymous
run around the house screaming
anonymous
  • anonymous
jump in mud, get paint all over my face!
anonymous
  • anonymous
oh this is AWESOME~
anonymous
  • anonymous
:O
anonymous
  • anonymous
lol
anonymous
  • anonymous
I can be pretty wild at times~
anonymous
  • anonymous
even though I sound so calm and innocent LOL, I can be devilish at times~ well.
anonymous
  • anonymous
depends on my mood ^_^"
anonymous
  • anonymous
sigh~
anonymous
  • anonymous
I feel better letting all this out, thanks for listening to all this crap lol :)
anonymous
  • anonymous
hope I didn't scare you? ._.
anonymous
  • anonymous
I AM SO SCARED!!
anonymous
  • anonymous
x_x I'm sorry
anonymous
  • anonymous
after what? :(
anonymous
  • anonymous
:(
anonymous
  • anonymous
T~T alright, no mud
anonymous
  • anonymous
I am setting at the corner covered by a blanket :(
anonymous
  • anonymous
>_> there are spiders there
anonymous
  • anonymous
OMG
anonymous
  • anonymous
can't believe you got scared from a girl ._.
anonymous
  • anonymous
LOL, awwww
anonymous
  • anonymous
LOL
anonymous
  • anonymous
don't worry, I'm not telling a soul ^_^
anonymous
  • anonymous
:) LOL!
anonymous
  • anonymous
girls are more Frightening than guys btw
anonymous
  • anonymous
well, not all girls :)
anonymous
  • anonymous
and let's just hope no one opens his/her group chat box ^_^
anonymous
  • anonymous
Generally speaking!!
anonymous
  • anonymous
and not all guys , lol
anonymous
  • anonymous
well, I don't fear anything, but God
anonymous
  • anonymous
^_^
anonymous
  • anonymous
mashallah :)
anonymous
  • anonymous
there's nothing to be afraid off as long as you know that you're protected by the almighty :)
anonymous
  • anonymous
When u do differentation u get 100000 as x for max(Y). but max x is only 60000, so, by substituting u get y=4, so total amt. p*x=240000.

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