Question

The demand for a product is given by p=50/√x for 1≤x≤8000 and the cost function is given by C=.5x+500 for 0≤x≤8000

Find the marginal profits for a) x=900 b) x=1600 c) x=2500 D) x=3600

If you were in charge of setting the price for this product what would you set? Explain your reasoning.

Answer 1

wow, i truly do enjoy your questions, they are really good application problems

Answer 2

It's from my calculus class and there's really only a few problems on each assignment that i dont understand.

Answer 3

Now, i am sure you are smart enough to realize that you have to find the function that gives you the marginal cost

Answer 4

thats the derivative of C?

Answer 5

i dont think its that simple this time, check your book does it give some steps for find the marginal cost function? i think i might know, but i just want to be sure

Answer 6

i only have that P'=marginal profit, R'=marginal revenue, and C'= marginal cost

Answer 7

and profit is given by P=R-C

Answer 8

thats the one

Answer 9

okay so then do i have to find revenue before i do anything else?

Answer 10

yes, we have to do R-C

Answer 11

now can you do that or should i help

Answer 12

when i find the revenue do i just start plugging in my numbers? or do i have to do something else??

Answer 13

when you find the revenue, get the first derivative and just start plugging in numbers

Answer 14

okay

Answer 15

if you want, let me know what you can so that i can double check :)

Answer 16

do i take the derivative of the revenue?

Answer 17

you take the derivaitve of P, which is given by R-C

Answer 18

what do i do with my p=50/\[\sqrt{x}\]

Answer 19

You are give:

P=50/SQRT(X)

C=0.5x+500

Answer 20

yes

Answer 21

you need to do: