Question

A price p (in dollars) and demand x for a product are related by
2x2+3xp+50p2=28000.

If the price is increasing at a rate of 2 dollars per month when the price is 20 dollars, find the rate of change of the demand.

Rate of change of demand =

Answer 1

are the x an p values squared?

Answer 2

is it 2x^2+3xp+5p^2=28000?

Answer 3

Please reply so that I can know to continue.

Answer 4

Anyways, So p=20 dp/dt=2 then find what you want to know and we want to know what dx/dt is, so differentiate the equation with respect to d/dt so we will get:

Answer 5

Sorry the equation is like 2x^2+3xp+50p^2=28000

Answer 6

2x dx/dt + 3x dp/dt +p dx/dt + 100p dp/dt = 0

Answer 7

oo i think I know where I went wrong.. I didn't do 3p dx/dt but plz continue as I have tried this question 3x and have diff results which are all wrong T.T

Answer 8

Also is it -3xp or +3xp?

Answer 9

+3xp
and shouldn't 2x dx/dt be 4x dx/dt?

Answer 10

ok

Answer 11

Let me start over

Answer 12

p and x are functions of t, so step 1 take the derivative of both sides

Answer 13

d/dt(2x^2+3xp+50p^2)=d/dt(28000)

Answer 14

You get 4xx' +3x'p+3xp'+100pp'=0

Answer 15

now factor our x'

Answer 16

Are you following so far?

Answer 17

yeah I got that far

Answer 18

ok

Answer 19

(4x+3p)x'+(3x+100p)p'=0

Answer 20

then isolate right?

Answer 21

(4x+3p)x'=-(3x+100p)p'

Answer 22

x'=-(3x+100p)p'/(4x+3p)

Answer 23

That would be part 1

Answer 24

ok yeah this is exactly what I did - it ends up getting x=80 but plz continue

Answer 25

now part 2. p=$20,

Answer 26

2x^2+3x(20)+50(20)^2=28000.

Answer 27

2x^2+60x+20000=28000

Answer 28

2x^2+6x-8000=0

Answer 29

x^2+3x-4000=0

Answer 30

Now factor

Answer 31

60 goes to 30

Answer 32

one sec

Answer 33

it should be x^2+30x-4000

Answer 34

ok

Answer 35

nice catch

Answer 36

and yeah I screwed up a sign in that equation maybe that's where I went wrong and tyty

Answer 37

(x-50)(x+80)=0

Answer 38

So x can be -80 and 50

Answer 39

but it must be positve so its 50

Answer 40

So now you know p=$20, p'=$2 per month, x =50 units

Answer 41

now plug this into the previous x'

Answer 42

x'=-(3(50)+100(20))(2)/(4(50)+3(20))

Answer 43

solve it and it would give you the units per month

Answer 44

omg kk thank you so much!!! I got it right! So how do I give you a good testimonial and all? hahahah

Answer 45

Um, I guess you could do it if you click on my name. But I think you have to become a fan first. Something like that

Answer 46

Ok became a fan! thanks again!

Answer 47

yep, glad to help