Find ans classify the stationary points for the following functions:

Q= 5㏑L + 2㏑K - 0.1L - 0.4K

- Sep 21st 2008, 05:55 PMsennachanFind ans classify the stationary points for the following functions
Find ans classify the stationary points for the following functions:

Q= 5㏑L + 2㏑K - 0.1L - 0.4K - Sep 22nd 2008, 03:39 AMticbol
If that is

Q = 5L^2 +2K^2 -0.1L -0.4K

then,

get the partial derivatives of Q with respect to L and K, and set those to zero.

Let me express "partial deivative of Q with respect to L" as DQ/DL, so,

DQ/DL = 10L -0.1

0 = 10L -0.1

L = 0.1/10 = 0.01

DQ/DK = 4K -0.4

0 = 4K -0.4

K = 0.4/4 = 0.1

Thus, for those values,

Q = 5(0.01)^2 +2(0.1)^2 -0.1(0.01) -0.4(0.1) = -0.0205

Hence, if the point is expressed in (L,K,Q), then,

(0.01, 0.1, -0.0205)

is the stationary point.

To check if if it is maximum, minimum or a saddle point, we look at the second partial derivatives.

D/DL of DQ/DL = 10 ......positive

D/DK of DQ/DK = 4 .......positive also

Meaning, the stationary point could be a minimum.

Let's chect the mixed partial,

D/DL of DQ/DK = 0

So

(10)(4) -0 = 40 ......positive

Meaning, the stationary point is really a minimum point.