# Thread: Need help with linear programming problem

1. ## Need help with linear programming problem

Can you give me quickly some tips on how to solve this:

2. A look at the vector a, should make this problem much easier to solve.

$\displaystyle [1, 0 \dots 0]^T $\begin{bmatrix} x_{11} & \dots & x_{1n} \\ \vdots & & \vdots \\ x_{n1} & \dots & x_{nn} \end{bmatrix}$$$\displaystyle $\begin{bmatrix}b_1 \\ \vdots \\ b_n\end{bmatrix}$$
$\displaystyle = [1, 0 \dots 0]^T $\begin{bmatrix}b_1x_{11} + \dots b_nx_{1n} \\ \vdots \\ b_1x_{n1} + \dots + b_nx_{nn} \end{bmatrix}$$
$\displaystyle = $\begin{bmatrix}b_1x_{11} + \dots + b_nx_{1n} \\ 0 \\ \vdots \\ 0 \end{bmatrix}$$

So your objective function becomes $\displaystyle b_1x_{11} + \dots + b_nx_{1n}$
and your constraints are only the ones that apply to the variables in the objective function.

$\displaystyle x_{11} + \dots + x_{1n} = 1$

$\displaystyle 0 \leq x_{1i} \leq 1$ for $\displaystyle 1 \leq i \leq n$

I am not sure how you're supposed to solve the problem, but I'm pretty sure this set up is correct.