# Homework Help: Linear programming

1. Feb 17, 2008

### Freydulf

1. The problem statement, all variables and given/known data

Solve:

http://www.rinconmatematico.com/latexrender/pictures/0399b7f0b179dcbf396e72f315e6d219.png [Broken]

2. Relevant equations

3. The attempt at a solution

http://www.rinconmatematico.com/latexrender/pictures/5a8e45f50b7d55e4c8ab2c5ce3b7d554.png [Broken]
http://www.rinconmatematico.com/latexrender/pictures/dfd7077296a65ae4d3a0b0f409ef0118.png [Broken]

http://www.rinconmatematico.com/latexrender/pictures/be995f308f56dfd08931544079d643eb.png [Broken]

http://www.rinconmatematico.com/latexrender/pictures/76941dbf58eb6b6a6a5abb3f76c2326c.png [Broken]
http://www.rinconmatematico.com/latexrender/pictures/8b328666878b3c586f55614fc7162373.png [Broken]

http://www.rinconmatematico.com/latexrender/pictures/3846f3e2531e839b39ea7f5626b7c0ef.png [Broken]

Positive-semidefinite, it has a global minimum at (0,0).

Well, that's what I've done til now. I'm not sure whether it's right, can someone give me a hand? :)

Last edited by a moderator: May 3, 2017
2. Feb 18, 2008

Can you explain what you're trying to do? It's hard to help without understanding your approach.

I'm guessing you're trying to show that the function has a positive semi-definite Hessian, which implies convexity, which implies global minimum. However, what you have there is certainly not positive semidefinite.

Do you really believe this? You are essentially saying that both the function $z^3$ and the function $-z^3$ are both non-negative for all z.

Assuming you're trying to look at the Hessian, try differentiating again. It contains SECOND derivatives.

Last edited by a moderator: May 3, 2017
3. Feb 18, 2008

### HallsofIvy

This is certainly NOT "linear programming". Your equations are not linear.