Question

I really need some help with this its a calculus problem.
The demand for a product is given by the equation 10p + x = 40000, and the cost for producing the product is given by C(x) = 2000x + 30000.
a. Find the rate of change of the profit, when the number of units produced is 1000 and the number of units produced is decreasing at a rate of 50 units per week.












b. Find the rate of change of the number of units produced per week when the number of units produced is 5000, and the profit is increasing at a rate of $50000 per week.

Answer 1

Any idea ?

Answer 2

one sec I think I can help with this

Answer 3

ok thanks mathdood

Answer 4

np

Answer 5

so x is the number of units what is p?

Answer 6

p is demand I believe that's what it usually stands for when we did problems

Answer 7

or maybe its profit ? I know I sound stupid whatever seems right

Answer 8

haha no

Answer 9

ok so its demand?

Answer 10

I meant no you don't sound stupid. I am not sure what it stands for.

Answer 11

because it doesn't say what p is I think we have to know that

Answer 12

demand sounds right though.

Answer 13

Ok

Answer 14

So let me put some effort here as well demand would be p = -x/10 + 4

Answer 15

okay I don't know why I didn't realize this right away but it has to be demand because it is the equation for demand and there is only two variables and x we already know is the number of units because of the cost equation lol. So rearrange for p to get p = (40000-x)/10

Answer 16

Ok got that part now

Answer 17

then what?

Answer 18

One sec I am sort of taking this as I go I havent done one of these in a while.

Answer 19

Oh ok sorry

Answer 20

wait a sec how much does the product cost? I mean to the people buying it?

Answer 21

The cost for producing it is not the same as the price it is sold for without this information you can't answer the question.

Answer 22

There is no cost for people buying it when I asked for help from someone else for part a they took profit function to be 4000 - x/5 - 2000

Answer 23

and plugged in 1000 for x and got 1800

Answer 24

but I did not get why so I wanted a second feedback/ help

Answer 25

Okay there has to be a price for the product if people aren't paying there would be no profit. In order to find the equation for profit you need to know two things; 1. How much it costs to produce the product and 2. how much the product is being sold for. Maybe I am misunderstanding the question though. I will keep trying.

Answer 26

maybe x is the demand for the product and p is profit? Then this would make more sense.

Answer 27

Exactly, I know what you mean but the teacher said theres no error in problem

Answer 28

okay well if p stands for profit then you would just take the derivative of p = (40000-x)/10 first do you know how to do this?

Answer 29

Yeah that would be -1/10 right

Answer 30

right sorry I am messing you up real bad here is this a related rates problem ?

Answer 31

Yeah this is a related rates!

Answer 32

No i am just lost and frustrated

Answer 33

it looks like a related rates problem one sec one more time haha lol o man okay I can do this

Answer 34

Oh ok :) Yesss

Answer 35

okay we know that x' = 50 right?

Answer 36

like the derivative of x = 50 because the rate of change of x for the problem is 50 do you understand what I am saying? and x = 1000 because the amount of products at that instant is 1000. Are we clear so far?

Answer 37

Yeah I get that!

Answer 38

where'd you go?!

Answer 39

haha okay nvm I get what you are saying so far

Answer 40

alright now we need to find the equation that relates the profit to the number of units being produced but it looks like we are back to square one because the x has to be the number of units being produced so p has to be the demand it just really seems like there is a crucial peice of information missing here

Answer 41

damn okay

Answer 42

If I knew what the price of the product was then I would go price of the product times x minus the cost of producing the product. Then I would do some other stuff and do implicit differentiation and solve for the rate of change of the profit or something that is usually how rate of change problems go but this problem has me stumped for some reason. Sorry Ill be back in a minute I have to go eat.

Answer 43

Okay no problem I'll ask the teacher

Answer 44

Thanks for the great effort please add more if you do figure it out

Answer 45

p=price, x=units produced demand = 40000 price = 3900 profit = pricex - costx so profit = 3900x - 2000x^2+30000x and profit' = 3900x'-4000xx' + 30000x' then you just fill in your numbers this is the only way I can make sense of this problem demand must be a constant number and price and units are dependant on the demand that why they showed it as 10p + x = 40000

Answer 46

except when I fill in the number the answer looks totally wrong

Answer 47

oh i seee

Answer 48

When you find out what the answer is would you post it so I could see because this seems like it should have been a straight forward problem.

Answer 49

Yeah no I definitely will let you know tomorrow!

Answer 50

awesome thanks it drives me nuts when I can't figure somethin out haha

Answer 51

This is why I dislike math sometimes I study so much and then this

Answer 52

yaeh i feel u