TITLE: Solving this linear programming takes forever... is there a more efficient way to solve it?
QUESTION [0 upvotes]: I'm supposed to solve the following LP:
$(P_2) \text{ } \text{max}\left\{ 33x_1+13x_2+18x_3 \mid \begin{matrix}
8x_1+3x_2+4x_3 \leq 32\\ 
12x_1+5x_2+7x_3 \leq 51\\ 
5x_1+2x_2+3x_3 \leq 21\\ 
x_1+x_2+x_3 \geq 3
\end{matrix} \right\}$
I have formed the inequations to equations:
$8x_1+3x_2+4x_3+y_1=32$
$12x_1+5x_2+7x_3+y_2=51$
$5x_1+2x_2+3x_3+y_3=21$
$-x_1-x_2-x_3+y_4=-3$
And the solution problem (on my paper "Zielfunktion") is $33x_1+13x_2+18x_3$
I'm supposed to solve it by using simplex algorithm. As you will see below, my solution is very long... I needed about 8 tables and our teacher said that it's solvable with maybe 3 tables. But how? :(
The yellow marks are the pivot elements.

REPLY [3 votes]: See picture below:

Hope this helps !
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