$(35)$ A farmer has some land and is considering to grow three types of crops $($wheat$,$ corn, and soybean$).$ The man$-$days, preparation cost and profit per acre for each crop is summarized in the table below. The maximum number of man$-$days available are $50$ and the farmer has $$600$ for preparation of the crop. The LP that maximizes the farmer's profit from the three crops is given on the right and the optimal tableau for this LP is provided below.

$\backslash$table$[[$Crop$,$Man$-$days,Preparation cost $($$$),$Profit $($$$)],[$Wheat$,2,3,12],[$Corn$,2,1,10],[$Soybean$,0,4,8]]$

The appropriate model of the problem and the final simplex table that gives the best solution are shown below.

MAxZ$=12x_1+10x_2+8x_3$

$s.t$

$2x_1+2x_{2}50$

$3x_1+x_2+4x_{3}600$

$x_1,x_2,x_{3}0$

$\backslash$table$[[,x_1,x_2,x_3,s_1,s_2,$ST$],[Z,?,0,0,?,?,?$