Question

The cost in dollars of producing x units of a product is given by
C(x) = \frac{7 x^2 - 27 x + 12}{3 \sqrt{x}} for x \ge 0.
Determine the value of x when the marginal cost is 0

Answer 1

Wow...that is a mess.

Answer 2

\[\frac{7 x^2 - 27 x + 12}{3 \sqrt{x}} for x \ge 0.\]This is it fixed.

Answer 3

I believe it's, anyways.

Answer 4

yes

Answer 5

Set the derivative to zero and find the value of x at that point?

Answer 6

Just wondering, that's undefined when x = 0, right? Did you mean x > 0?

Answer 7

x is more than or = to zero

Answer 8

@rukh - I can help you with the apartment problem too.

Answer 9

ok

Answer 10

That one, the occupancy equation is -8x + 960 (since at $960, you get zero occupancy). Rent revenue = -8x^2 + 960x. Differentiate and set to zero, you get x = 60 units. At x = 60 units, price = -480 + 960 = $480.

Answer 11

Revenue is maximized at price $480, which results in occupancy of 60 units.

Answer 12

thanks, that was correct...60 units

Answer 13

now what abt this on with margianl cos?

Answer 14

I am not too good with derivatives. Forgot long ago. But, to get marginal cost = 0, you are finding the tangent of the curve with slope = 0. That turns out to be the derivative of the cost function set to zero.

Answer 15

but then i get 2 values for x

Answer 16

and i dont think either one is the answer

Answer 17

What are the values?

Answer 18

GT, im curious how u know if derivative of c(x) gives u "marginal cost" ?

Answer 19

the derivative of cost is the marginal cost

Answer 20

Marginal cost = increase in cost to produce extra units of the product. That cost is zero where the "curve" flattens. That means, tangent to curve has slope zero.

Answer 21

so how do i calculate?

Answer 22

@saifoo.khan Can you help with derivative of this above function? Need values of x where that derivative is zero.

Answer 23

i c, gota review my english market vocabs =(

Answer 24

That's when:\[7x^{2} - 9x - 4 = 0\]as\[\frac{dC}{dx} = \frac{7x^{2} - 9x - 4}{2x^{3/2}}\]

Answer 25

how is dC/dx that?

Answer 26

ok so whats x?

Answer 27

I think you need to treat it as f(x) * g(x) where 7x^2-9x-4 is f(x) and 1/3x^1/2 is g(x) and apply d/dx(f(x)*g(x)) = f(x)*dg(x)/dx + g(x)*df(x)/dx.

Answer 28

I double checked my answer with the Wolf. Click show steps for derivation: http://www.wolframalpha.com/input/?i=d%28%287*x%5E2+-+27*x+%2B+12%29%2F%283*sqrt%28x%29%29%29%2Fdx

Answer 29

@GT , sorriieee. i just saw the notif.
do you need help now as well?

Answer 30

hey guys i have 4 mins to solve this problem before my hw expires :(

Answer 31

Well, yeah.

Answer 32

The derivative of that function.

Answer 33

wolf shows the steps as well, that will help.

Answer 34

@bmp - if it is when 7x2−9x−4=0, then quadratic roots of that are:
(9 +/- SQRT(81+112))/14
(9 +/- SQRT(193))/14
Since, x can't be negative, it has to be:
(9 + SQRT(193))/14.

Right.

Answer 35

1.635??

Answer 36

thanks

Answer 37

@GT I got the same value for x, at least. :-)

Answer 38

:)