This is the initial tableau of a linear programming problem

This is the initial tableau of a linear programming problem. Solve by the simplex method. [x_1 x_2 S_1 s_2 s_3 z 1 4 1 0 0 0 12 2 4 0 1 0 0 4 1 5 0 0 1 0 4 -2 -1 0 0 0 1 0] The maximum is when x_1 = x_2 = S_1 = 10, s_2 = 0, and s_3 = 2.

Solution

Table #1
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x1 x2 s1 s2 s3 z   
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1 2 1 0 0 0 12   
2 4 0 1 0 0 4
1 5 0 0 1 0 4
-2 -1 0 0 0 1 0

Table #2
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x1 x2 s1 s2 s3 z   
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0 0 1 -0.5 0 0 10   
1 2 0 0.5 0 0 2
0 3 0 -0.5 1 0 2
0 3 0 1 0 1 4

The solution of the given table is z = 4 when x1 = 2 and x2 = 0 obtained from above table