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Math Help - Need help with linear programming problem

  1. #1
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    Need help with linear programming problem

    Can you give me quickly some tips on how to solve this:
    Need help with linear programming problem-newbitmapimagen.png
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  2. #2
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    A look at the vector a, should make this problem much easier to solve.

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

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

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

     0 \leq x_{1i} \leq 1 for 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.
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