Solving this linear programming takes forever... is there a more efficient way to solve it?

Question

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.

Answer 1

See picture below:

Hope this helps !