max z 2 x 1 3 x 2 s t x 1 2 x 2 6 2 x 1 x 2 4 x 1 , x 2 0 The following Simplex tableau corresponds to a basic feasible solution to the LP problem above Row z x 1 x 2 s 1 s 2 RhsBV01 0 501 509 z 100 510 503 x 2 201 50 0 511 s 2 According to this Simplex Tableau, this basic feasible solution is x 1 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456, x 2 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456, s 1 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456, and s 2 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 In this basic feasible solution, variables s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 are basic variables, and variables s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 are nonbasic variables To move to a better adjacent basic feasible solution, variable s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 is the entering variable (i e , entering the basis), and variable s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 is the leaving variable (i e , leaving from the basis) The Simplex tableau for the better adjacent basic feasible solution is Row z x 1 x 2 s 1 s 2 RhsBV01 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 z 10 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 x 2 20 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 x 1

Question

max z   2 x 1   3 x 2 s t  x 1   2 x 2 6 2 x 1   x 2 4 x 1 , x 2 0 The following Simplex tableau corresponds to a basic feasible solution to the LP problem above  Row z x 1 x 2 s 1 s 2 RhsBV01 0 501 509 z 100 510 503 x 2 201 50 0 511 s 2 According to this Simplex Tableau, this basic feasible solution is x 1   s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456, x 2   s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456, s 1   s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456, and s 2   s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456  In this basic feasible solution, variables s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 are basic variables, and variables s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 are nonbasic variables  To move to a better adjacent basic feasible solution, variable s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 is the entering variable (i e , entering the basis), and variable s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 is the leaving variable (i e , leaving from the basis)  The Simplex tableau for the better adjacent basic feasible solution is  Row z x 1 x 2 s 1 s 2 RhsBV01 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 z 10 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 x 2 20 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 s1s2x1x2s1 and s2s1 and x1s1 and x2s2 and x1s2 and x2x1 and x2 3 2 5 2 1 0 5 1 301 32 314 31 55 328 3310 3456 x 1

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Question: max z = 2 x 1 + 3 x 2 s.t. x 1 + 2 x 2 6 2 x 1 + x 2 4

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