Question

For the given cost function
C(x) = 28900+600 x + x^2 find:
a) The cost at the production level 1850
b) The average cost at the production level 1850
c) The marginal cost at the production level 1850
d) The production level that will minimize the average cost
e) The minimal average cost

Answer 1

mostly i dont know how to solve d and e

Answer 2

ANYONE?

Answer 3

differentiate C(x) and equate this to zero
solving this for x will give you the production level you require
this is d)

Answer 4

plugging this value into C(x) will give you (e)

Answer 5

are you familiar with calculus ?

Answer 6

YES I AM AND I TRIED TO DIFFERENTIATE C(X) AND THEN SET TO 0 AND SOLVE AND I DIDNT GET THE CORRECT ANS

Answer 7

So what did you get when you took the derivative?

Answer 8

ITS 600+2X FOR THE DERIVATIVE

Answer 9

and with this derivative when u solve for x - it comes out to be -300. which is not correct according to my hw

Answer 10

Hmm that seems as if it should be correct, are you sure you have the correct function?

Answer 11

yes...its C(x) = 28900+600 x + x^2

Answer 12

with the given function the derivative will be \[2x+600\] then set to 0 will give you \[x=-300 \]

Answer 13

Average Cost = c' (x) / x
= (2x + 600 ) / x
= 2 + ( 600/ x )

Answer 14

Chlorophyll how would i find x? set the average cost = 0?

Answer 15

this gives -300 which isnt correct :(

Answer 16

aah the average cost

Answer 17

Hold on, I'm thinking!

Answer 18

ok thanks a bunch!

Answer 19

Average Cost = cost/ quantity

Answer 20

http://faculty.wlc.edu/buelow/calc/nt4-7.html This is a site that explains this principle.
It is easier to post this than to type it out.

Answer 21

= ( 28,900+600 x + x^2 )/ x
= x + 600 + ( 28,900 / x )

Answer 22

@ sashley0915 thanks

Answer 23

@sashley0915 That's just perfect :D

Answer 24

Hope it helps... :)

Answer 25

@rukh can you continue?

Answer 26

im trying

Answer 27

sigh....

Answer 28

Okie, let me give more hints ;)

Answer 29

ok :)

Answer 30

Take derivative of average cost
Avg (x) = x + 600 + ( 28,900 / x )
Avg' (x) = ( - 28,900 / x² ) + 1 = 0
=> x = √ 28,900 = 170 units

Answer 31

Now are you fine now?

Answer 32

\[\text Avg cost = \frac{C(x)}{x}\]
differentiate using quotient rule, and set equal to zero
\[\frac{x*C'(x) - C(x)}{x^{2}} = 0\]
\[x*C'(x) - C(x)= 0\]
\[C'(x) = \frac{C(x)}{x}\]
so you see that avg cost is minimized when it equals marginal cost

Answer 33

thanks everyone