Determine whether the given simplex tableau is in final form. If so, find the so

Question

Determine whether the given simplex tableau is in final form. If so, find the solution to the associated regular linear programming problem. If not, find the pivot element to be used in the next iteration of the simplex method.

Determine whether the given simplex tableau is in final form. If so, find the solution to the associated regular linear programmin g problem.If not, find the pivot element to be used in the next iteration of the simplex method. x y zuV P Constant 3 0 5 1 1 0 26 2 1 3 0 1 018 46 8 0 7 0 2 O Yes, the simplex tableau is in final form. The system has a maximum value of 46 at (26, 18, o) O Yes, the simplex tableau is in final form. The system has a maximum value of 46 at (8, 0, 7). O Yes, the simplex tableau is in final form. The system has a maximum value of 46 at (0, 18, 0) No, the simplex tableau is not in final form. The pivot element is 3 in the first row, first column. No, the simplex tableau is not in final form. The pivot element is 5 in the first row, third column.

Explanation / Answer

In the given problem,As there are no remaining negative numbers in the bottom row, this tableau represents the optimal solution.

To get the optimal solution, Locate the basic variables in final tableau.In this case the basic variables are y,u and P.The basic variables are those heading unit columns.Notice that y,u and P has unit columns.All the other variables are non basic.So the solution of non basic variables is 0. i.e x=0,z=0 and v=0.

The value assigned to basic variable y is 18 since y is a unit column and 1 is in the second row which has constant 18.So y=18.Similarly, The value assigned to basic variable u is 26 and likewise P=46

To conclude

Yes, the simplex tableau is in final form.The system has a maximum value of 46 at (0,18,0) we only consider x,y,z in final solution.

x y(unit column) z u(unit column) v P(unit column) constant 3 0 5 1 1 0 26 2 1 3 0 1 0 18 8 0 7 0 2 1 46

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