Find the pivot element to be used in the next iteration of the simplex method.
A) Pivot element is 3, lying in first row, second column
B) Pivot element is 0, lying in second row, second column
C) Pivot element is 1, lying in third row, second column
D) Pivot element is , lying in first row, first column
E) Pivot element is 1, lying in fourth row, second column

Question

Find the pivot element to be used in the next iteration of the simplex method. 
A) Pivot element is 3, lying in first row, second column 
B) Pivot element is 0, lying in second row, second column 
C) Pivot element is 1, lying in third row, second column 
D) Pivot element is , lying in first row, first column 
E) Pivot element is 1, lying in fourth row, second column

Quizplus · Accepted Answer

In the simplex method, we choose the pivot element as the most negative number in the bottom row (except for the last column, which indicates the constant terms). In this case, the most negative number is -1 in the second column, so we need to choose the row with the smallest non-negative ratio between its constant term and its entry in the second column. The ratios for the second column are 3/3=1 for the first row, 0/(-1)=0 for the second row, 1/1=1 for the third row, and 2/2=1 for the fourth row. Since the ratio is smallest for the second row and it is the only one with a 0 in the second column, we choose the pivot element to be 1 in the second column, which lies in the third row. Therefore, the answer is C.

Find the Pivot Element to Be Used in the Next