# Math Help - Linear Progamming

1. ## Linear Progamming

I need your help to solve the following
Given $Bx \leq b$ (1)

Consider the linear programming problem $\max \{1.y:Bx+y-\beta b \leq 0, 0 \leq y \leq 1, \beta \geq 1\}$ (2)

a. Suppose that (2) is feasible and $(x^*,y^*,\beta^*)$ is an optimal solution. Prove that $y^*_i$ if and only if $B_ix \leq b_i$ is an implicit equality of (1).

b. Prove that the optimal solution of the linear programming problem (2) determines which inequalities from $Bx \leq b$ are always satisfied with equality.

Thank you.

2. ## Re: Linear Progamming

What do you mean by "prove $y_i^*$"? Prove that it has what property?

3. ## Re: Linear Progamming

$y^*=(y^*_k)$