Courses   <-  Sean Forman   <-  You Are Here Choosing the Pivot Column and Row

MAT 1151, Business Math, Sean Forman

For the following tableau, circle the pivot column (if one exists) and the pivot row (if one exists). If there is no pivot column, we know the tableau is the final, optimal solution. If there is no pivot row, we know that no solution exists.

Rules

• The pivot column is the column with the most negative entry in the bottom row. If there is a tie, choose the one furthest to the left.

• The pivot row is row with the minimum value of $\frac{b}{a}$. Where $b$ is the right-hand side value and $a$ is the value in the pivot column. $a$ must be greater than zero for that row to be considered. If there is a tie choose the upper row.

1. 	$x_1$	$x_2$	$x_3$	$s_1$	$s_2$
   $s_1$	1	1	2	1	0	6
   $s_2$	1	1	3	0	1	7
   $P$	-6	-5	-3	0	0	0

   
   
   
   

2. 	$x_1$	$x_2$	$x_3$	$s_1$	$s_2$
   $s_1$	1	2	2	1	0	8
   $s_2$	1	1	3	0	1	6
   $P$	6	-5	-3	0	0	0

   
   
   
   

3. 	$x_1$	$x_2$	$x_3$	$s_1$	$s_2$
   $s_1$	1	1	2	1	0	6
   $s_2$	1	-1	3	0	1	3
   $P$	-2	-5	-4	0	0	0

   
   
   
   

4. 	$x_1$	$x_2$	$x_3$	$s_1$	$s_2$	$s_3$
   $x_1$	1	2	2	1	0	0	6
   $s_2$	0	$\frac{1}{2}$	3	4	1	0	3
   $s_3$	0	3	3	4	0	1	27
   $P$	0	-5	-4	-3	0	0	36

   
   
   
   

5. 	$x_1$	$x_2$	$x_3$	$s_1$	$s_2$
   $x_3$	0	1	1	1	3	6
   $x_1$	1	-1	0	4	1	3
   $P$	0	5	0	3	2	48

   
   
   
   

6. 	$x_1$	$x_2$	$x_3$	$s_1$	$s_2$
   $x_3$	0	2	1	1	3	6
   $x_1$	1	3	0	4	1	3
   $P$	0	-5	0	3	2	48

   
   
   
   

7. 	$x_1$	$x_2$	$x_3$	$s_1$	$s_2$
   $x_3$	0	-2	1	1	3	6
   $x_1$	1	-3	0	4	1	3
   $P$	0	-5	0	3	2	48

   
   
   
   

8. 	$x_1$	$x_2$	$x_3$	$s_1$	$s_2$
   $s_2$	0	1	1	1	1	6
   $x_1$	1	-1	1	4	0	3
   $P$	0	5	-3	3	0	18