Given the tableau

Question

Given the tableau

	2	5	3	1	0	0	0			9
	3	2	4	0	1	0	0			32
	2	4	3	0	0	1	0			24
	-6	-4	-8	0	0	0	1			0

1. This Tableau has no solutions
2. 
   
3. This Tableau has no more pivots and the final answer is:
4. 
   
5. This Tableau can pivot and the result of the pivot is:
6. 
   

The pivot point is: (write as an ordered pair.)

Answer 1

Looking at this simplex tableau, I need to determine if it can pivot and identify the pivot point.

Analysis of the Current Tableau

The tableau shows:

1. Bottom row (objective row): -6, -4, -8, 0, 0, 0, 1, [empty], [empty], 0, [empty]
2. Three constraint rows with RHS values: 9, 32, 24

Determining if Pivoting is Possible

For a maximization problem, we can pivot if there are negative coefficients in the objective row (excluding the rightmost value).

The objective row has: -6, -4, -8 (all negative)

This means the tableau CAN pivot.

Finding the Pivot Point

Step 1: Select the entering variable (pivot column)

1. Choose the most negative coefficient: -8 (column 3)
2. Entering variable is in column 3

Step 2: Select the leaving variable (pivot row) - Minimum Ratio Test

Calculate ratios of RHS to pivot column values (only for positive entries):

1. Row 1: 9/3 = 3
2. Row 2: 32/4 = 8
3. Row 3: 24/3 = 8

The minimum ratio is 3 (Row 1).

The pivot point is: (1, 3) - meaning Row 1, Column 3

The pivot element is the value 3 in the first constraint row, third column.

Answer: This tableau can pivot and the result of the pivot is a new tableau with the entering variable (column 3) becoming basic and replacing the variable that was basic in row 1.

The pivot point is: (1, 3) or (row 1, column 3)