Question

Shark Inc. has determined that demand for its newest netbook model is given by lnq−3lnp+0.003p=7, where q is the number of netbooks Shark can sell at a price of p dollars per unit. Shark has determined that this model is valid for prices p≥100. You may find it useful in this problem to know that elasticity of demand is defined to be E(p)=dq/dp (p/q)

a)Find E(p)
Your answer should only be in terms of p

b)What price will maximize revenue.

Answer 1

I have the same question with slightly different numbers, do you have any idea on how to get started on it?

Answer 2

i do but the webwork says i got the wrong answer.

Answer 3

what about you?

Answer 4

I have no clue. apparently I'm supposed to differentiate the function first, and then plug it into the E(p) ?

Answer 5

yes, thats what i did

Answer 6

well, i think

Answer 7

are you in 104?

Answer 8

yeah

Answer 9

did you get the other ones?
I got all but 2 and half

Answer 10

I only have this question and 15 left.

Answer 11

I got the function for the first blank of this question, do you know how to get the price for maximizing revenue?

Answer 12

i got 3 - 0.003*p for my first blank. which is wrong.

Answer 13

my first blank is p(5/p - 0.004)

Answer 14

did you get it right?

Answer 15

yeah

Answer 16

wait i think i got this. give me a minute

Answer 17

is it p[(5)/(p-0.004)] OR p[(5/p)-0.004]?

Answer 18

The second one.

Answer 19

okay i got it too. the first one. I'm working on the second

Answer 20

I got the second one.

Answer 21

how??

Answer 22

maximum revenue is at unit elasticity which is equal to 1, but for some reason you have to make it equal to -1

Answer 23

just set the function you just found equal to -1 and solve for p

Answer 24

so p[(5/p)-0.004]=-1?

Answer 25

yeah

Answer 26

Also, can you tell me the answers to the blanks of Question 15?

Answer 27

im not able to do it either

Answer 28

we could guess the third one though

Answer 29

apparently you find the Q'(p) and plug everything into the E(p) function that is given

Answer 30

That solves for E, then you take the derivative of E twice for the two blanks

Answer 31

did you get anything out?

Answer 32

I'm trying it.

Answer 33

ok i will too

Answer 34

a and b are just numbers so when you find the derivative of Q(p) , keep that in mind

Answer 35

I get Q'(p) = -b, what do you get?

Answer 36

same

Answer 37

plug it into E now i think

Answer 38

if you say so

Answer 39

so E = -bp/a-bp ??

Answer 40

wait

Answer 41

yes

Answer 42

now we're supposed to take the derivative, and then the 2nd derivative

Answer 43

of -bp/a-bp right

Answer 44

yeah

Answer 45

(d)/(db)(-(b p)/a-b p) = -((a+1) p)/a ?

Answer 46

uh i got soething different

Answer 47

watcha get?

Answer 48

plug it in and see if its right

Answer 49

i got, -ba/(a-bp)^2

Answer 50

Plugged it in, it's right

Answer 51

hurray!!

Answer 52

second deriv now

Answer 53

k

Answer 54

Who's your prof btw?

Answer 55

pfeiffer. yours?

Answer 56

Iain moyles

Answer 57

hmm

Answer 58

did you get it

Answer 59

I got -3ba(a-bp)/(a-bp)^4

Answer 60

Going to try it

Answer 61

ok

Answer 62

It's wrong

Answer 63

yup me too

Answer 64

Hold on, so Uprime is 0
V prime is 2(a-bp)(-b) right?

Answer 65

right

Answer 66

so when I do the top I get ba * -2b(a-bp)

Answer 67

ok...

Answer 68

is that right?

Answer 69

seems to be. yeah

Answer 70

nevermind that was wrong i got it

Answer 71

-2b^2a(a-bp)/(a-bp)^4

Answer 72

The (a-bp) on the top cancels out with one on the bottom

Answer 73

Answer is -2b^2a/(a-bp)^3

Answer 74

ill check it

Answer 75

yipeeee!!!!

Answer 76

Finally.

Answer 77

so for the last one, i think its either a or d

Answer 78

It's d, I just guessed

Answer 79

great!!

Answer 80

hey, did you get the bacteria culture question?
i got all but one blank

Answer 81

yeah im done everything

Answer 82

The count in a bateria culture was 200 after 15 minutes and 1500 after 40 minutes. What was the initial size of the culture? Find the doubling period. Find the population after 120 minutes. When will the population reach 11000.

Answer 83

are your numbers same?

Answer 84

no they're different

Answer 85

i need to find population after 120 mins.

Answer 86

you got the formula?

Answer 87

just plug in 120 minutes for the formula you found

Answer 88

P=60e^(0.0806x120)??

Answer 89

Uh I did it different to find the formula. I used y=yknotb^kt

Answer 90

i dont know how to do that

Answer 91

dont you use A=Pe^(rt) formula?

Answer 92

no, you use the one i said, I am pretty sure, I don't know about that way.

Answer 93

http://answers.yahoo.com/question/index?qid=20110528012541AAZjVzB

Answer 94

Use that for help

Answer 95

ha. perfect

Answer 96

Gotta go, it's really easy. My values were 100 after 15 minutes and 1200 after 35 minutes. Take these and use 1200 as the Y and 100 as the Yknot

Answer 97

So mine went like 1200 = 100b^r(35-15)

Answer 98

And solved for r