Total production function using Lagrange Multipliers

[s3a]

Homework Statement

Attached as Question.jpg.

Homework Equations

Partial differentiation.
Lagrange multiplier equation.

The Attempt at a Solution

Attached as MyWork.jpg.

Is my work correct? I'm still not confident with myself for these problems and it would be great if someone could confirm if I did this problem correctly and also, the values (or value since I can ignore the negative because it makes no sense in the problem) I get seem rather strange and, knowing my teacher, he usually gives problems with numbers that work out well and his notes also have nicely fitting numbers.

 

[Ray Vickson]

Homework Statement

Attached as Question.jpg.

Homework Equations

Partial differentiation.
Lagrange multiplier equation.

The Attempt at a Solution

Attached as MyWork.jpg.

Is my work correct? I'm still not confident with myself for these problems and it would be great if someone could confirm if I did this problem correctly and also, the values (or value since I can ignore the negative because it makes no sense in the problem) I get seem rather strange and, knowing my teacher, he usually gives problems with numbers that work out well and his notes also have nicely fitting numbers.

You made a blunder: you started with
L = 12 x^{3/4}\, y^{1/4} + \lambda (100 x + 180 y - 25200) and wrote
\partial L/\partial y = 12 x^{3/4}\, y^{-1/4} + 180 \lambda,
which is incorrect.

RGV

 

[s3a]

Actually, I don't think so. (If that sounds rude, I don't intend to.)

Looking back at my work here, I see a coefficient of 3 and not 12 for L_y.

Could you tell me if I am right or wrong about this please?

 

[Ray Vickson]

Actually, I don't think so. (If that sounds rude, I don't intend to.)

Looking back at my work here, I see a coefficient of 3 and not 12 for L_y.

Could you tell me if I am right or wrong about this please?

You are wrong. Go back and look at what you wrote in the third line of your attachment.

RGV

 

[s3a]

I marked it in red to show what I am talking about in case we're mis-communicating. (It seems to be the third line too.)

 

[Ray Vickson]

I marked it in red to show what I am talking about in case we're mis-communicating. (It seems to be the third line too.)

I was not referring to the "3"; I was referring to the y^{-1/4}.

RGV

 

[HallsofIvy]

Yes, you have "3" correctly. However, your power of y is wrong. 1/4- 1 is not equal to -1/4.

 

[s3a]

Oh, yeah, oops. :shy:

Is the current attached work correct?