Check that the given simplex tableau is not in final form. Find the pivot element to be used in the next iteration of the simplex method.
A) pivot element is 5, lying in the third row, third column.
B) pivot element is 0, lying in the first row, third column.
C) pivot element is 5, lying in the third row, second column.
D) pivot element is 2, lying in the first row, second column.

Question

Check that the given simplex tableau is not in final form. Find the pivot element to be used in the next iteration of the simplex method. 
A) pivot element is 5, lying in the third row, third column. 
B) pivot element is 0, lying in the first row, third column. 
C) pivot element is 5, lying in the third row, second column. 
D) pivot element is 2, lying in the first row, second column.

Quizplus · Accepted Answer

The tableau is not in final form because there is at least one negative coefficient in the objective row (bottom row).
To find the pivot element, we look for the most negative ratio of the right-hand side to the corresponding coefficient in the pivot column (in this case, the third column).

For row 1, the ratio is undefined since the corresponding coefficient in the pivot column is 0. 
For row 2, the ratio is 8/2 = 4.
For row 3, the ratio is 11/(-2) = -5.5.
For row 4, the ratio is 15/4 = 3.75.

Therefore, the most negative ratio is in row 3, which means the pivot element is the coefficient in row 3 and column 2, which is 5.

Check That the Given Simplex Tableau Is Not in Final