## anonymous 5 years ago 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.

1. amistre64

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

2. amistre64

errr.. a negative slope lol;

3. amistre64

p = -(1/100000) x + 10

4. amistre64

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

5. amistre64

or am i missing something

6. anonymous

no

7. anonymous

8. amistre64

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

9. anonymous

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

10. anonymous

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

11. amistre64

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

12. anonymous

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

13. amistre64

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

14. anonymous

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

15. anonymous

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

16. 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?

17. anonymous

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

18. 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...

19. anonymous

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

20. 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

21. anonymous

Alright, now I got what you mean lol proceed ^_^

22. amistre64

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

23. anonymous

so we'll integrate from 0->6000?

24. amistre64

dunno if we integrate of simply anchor it in at (0,60000) p=10-(x/10000)

25. amistre64

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

26. amistre64

10(1000) - (1000)(1000)/2(10000) 10000 - 500/10

27. amistre64

10000 - 50 = 9950 +C

28. amistre64

P(1000) = 60000 = 9950 + C C = 60000 - 9950 = 50050 P(x) = 10(x) - x^2/20000 + 50050 ??

29. amistre64

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

30. anonymous

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

31. anonymous

LOL!

32. anonymous

do you know what I think?

33. amistre64

broken question? lol

34. anonymous

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

35. anonymous

.-. right?

36. amistre64

maximum price = 600,000? or max revenue?

37. amistre64

see the wording is off...

38. 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...

39. anonymous

so the maximum values for x and p : x = 0, and p = 10

40. 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

41. anonymous

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

42. dumbcow

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

43. amistre64

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

44. anonymous

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

45. 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)

46. anonymous

annnnnnwaaaar~ lol ^_^

47. anonymous

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

48. 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).

49. dumbcow

60,000 available not sold

50. anonymous

so how did you get 50k?

51. amistre64

i understand it now.... i think lol

52. dumbcow

differentiate above function set =0 solve for x

53. anonymous

p = 0 and solve for x?

54. amistre64

whoever wrote this problem could have been clearer ;)

55. anonymous

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

56. 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.

57. anonymous

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

58. anonymous

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

59. anonymous

LOL!!

60. anonymous

You're welcome. Am I right there?

61. anonymous

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

62. anonymous

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

63. anonymous

but it looks right though ^_^

64. amistre64

i was watching the cheerleaders and got distracted lol

65. anonymous

LOL

66. anonymous

HAHA.

67. dumbcow

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

68. 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!

69. anonymous

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

70. anonymous

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

71. anonymous

i get it thanks

72. anonymous

loooooooooooong morning, it was HILARIOUS

73. anonymous

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

74. anonymous

You have no more classes?

75. anonymous

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

76. anonymous

and guess what!

77. anonymous

what?!

78. 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? ^_^

79. anonymous

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

80. 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.

81. anonymous

lol.....LOL!

82. anonymous

LOL

83. anonymous

why did he call himself dumbcow?! :D

84. anonymous

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

85. anonymous

I have no idea.

86. anonymous

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

87. anonymous

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

88. anonymous

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

89. anonymous

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

90. anonymous

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

91. anonymous

neither

92. anonymous

all they say is mooo

93. anonymous

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

94. anonymous

with different wavelengths ~

95. anonymous

But I like it :)

96. anonymous

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

97. anonymous

omg..I sound drunk LOL with bananas~

98. anonymous

Nope, it's not.

99. anonymous

wait what?o_o

100. anonymous

yes it is

101. anonymous

102. anonymous

how can bananas get you drunk?

103. anonymous

lol. Yes, your theorem makes sense :P

104. 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? ._.

105. anonymous

see, I told you so , I told you so, I told you so~

106. anonymous

omg...please, bare with me this time and you'll never see me talk like this again >_<, I apologize guys

107. anonymous

never eat bananas in the morning = lesson of today

108. anonymous

You didn't say anything wrong!!

109. anonymous

I sound DRUNK LOL

110. anonymous

I don't eat bananas at all

111. anonymous

I don't know how "drunk people" sound. So, I don't knwo if you do sound like one :)

112. anonymous

know*

113. 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~

114. anonymous

lol

115. anonymous

I'm just having one of my childish moments right now ^_^"

116. anonymous

o_o...

117. anonymous

lol?

118. anonymous

These are the best moments. Enjoy them as much as you can

119. anonymous

and you + mr"dumbcow" are getting a medal for soling the questionariO~

120. anonymous

sigh~ I just need a break

121. anonymous

I didn't get a weekend for 2 weeks now, and I need one

122. anonymous

:(

123. anonymous

busy busy, quizzes, tests, quizzes, tests, studies, da da da ~

124. anonymous

Have a day off yo!!

125. anonymous

but you know what?

126. 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

127. anonymous

that's it, one day off is all I need

128. anonymous

YAAY.. I love "off" days!!

129. anonymous

The one you make by yourself are the best <3

130. 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

131. anonymous

I KNOW!

132. anonymous

I want to do something crazy !

133. anonymous

I'll mis-match my clothes

134. anonymous

for a start LOL

135. anonymous

LOL.. Day off does not mean you just sleep all day long. It is just "freedom". You "DO" whatever you like

136. 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

137. anonymous

run around the house screaming

138. anonymous

jump in mud, get paint all over my face!

139. anonymous

oh this is AWESOME~

140. anonymous

:O

141. anonymous

lol

142. anonymous

I can be pretty wild at times~

143. anonymous

even though I sound so calm and innocent LOL, I can be devilish at times~ well.

144. anonymous

depends on my mood ^_^"

145. anonymous

sigh~

146. anonymous

I feel better letting all this out, thanks for listening to all this crap lol :)

147. anonymous

hope I didn't scare you? ._.

148. anonymous

I AM SO SCARED!!

149. anonymous

x_x I'm sorry

150. anonymous

after what? :(

151. anonymous

:(

152. anonymous

T~T alright, no mud

153. anonymous

I am setting at the corner covered by a blanket :(

154. anonymous

>_> there are spiders there

155. anonymous

OMG

156. anonymous

can't believe you got scared from a girl ._.

157. anonymous

LOL, awwww

158. anonymous

LOL

159. anonymous

don't worry, I'm not telling a soul ^_^

160. anonymous

:) LOL!

161. anonymous

girls are more Frightening than guys btw

162. anonymous

well, not all girls :)

163. anonymous

and let's just hope no one opens his/her group chat box ^_^

164. anonymous

Generally speaking!!

165. anonymous

and not all guys , lol

166. anonymous

well, I don't fear anything, but God

167. anonymous

^_^

168. anonymous

mashallah :)

169. anonymous

there's nothing to be afraid off as long as you know that you're protected by the almighty :)

170. 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.