Math Is Fun Forum

carv

Member

Registered: 2011-07-25

Posts: 2

Linear Programming: finding objective function

It's a linear programming problem, could someone please help me to solve it? It's not about just the answer, but a way to do it. I'm just starting to learn LP.

My answer: Yes, it is. Using the values of x into the inequalities they are all satisfied, and there's also an associated base with this extreme point. You can find the base using the standard form that adds slack variables to turn constraints into equations.

So the remaining question I can't answer is:

I'd like to solve this algebraically.

My approach was first transform the problem into its standard form, with slack variables:

Then I got the dual, maybe it'll be useful,

Once I have the solution (1,1,1,1), which is feasible and I may assume is optimal according to vector c that I'll find, may I use the Complementary Slackness Theorem which says:

Assume primal problem (P) has a solution

and dual problem (D) has a solution

.
1. If 

, then the jth constraint in (D) is binding.
2. If the jth constraint in (D) is not binding, then

.
3. If 

, then the ith constraint in (P) is binding.
4. If the ith constraint in (P) is not binding, then

.

?

So in this case,

. Not using the y surplus variables, now I have four

variables and four constants

; i,k = 1,...,4. But really it's not helping me at all, I don't know how to go on from here. Surely there's something that I'm missing. I'd appreciate your help.

Last edited by carv (2011-07-26 05:10:41)