Understanding the Simplex Method and Tableau Analysis

The video tutorial explores four examples of Tableau analysis using the Simplex method to determine if a maximum exists. It explains how to identify active and inactive variables and calculate the maximum value and its occurrence point. The tutorial also covers scenarios where no maximum exists due to an unbounded feasible region.

What is the first step in determining if a maximum exists in a Tableau?

• Verify that all variables are set to zero.

• Check if all entries in the top row are positive.

• Analyze the left side of the bottom row for non-negative entries.

• Ensure all columns have a single one and zeros.

How can you identify active variables in a Tableau?

• By checking if they are listed on the far right.

• By ensuring their columns contain only zeros.

• By finding columns with a single one and zeros.

• By checking if they are equal to zero.

In the first example, what is the maximum value of the objective function P?

• 350

• 450

• 100

• 225

In the second example, what are the values of the inactive variables x sub 1 and x sub 2?

• Both are equal to 100.

• Both are equal to 0.

• x sub 1 is 375 and x sub 2 is 125.

• x sub 1 is 125 and x sub 2 is 375.

What is the maximum value of P in the second example?

• 450

• 350

• 225

• 375

In the third example, what is the value of x sub 2 when the maximum occurs?

• 225

• 475

• 100

• 0

What is the maximum value of P in the third example?

• 350

• 450

• 100

• 225

What indicates that a feasible region is unbounded in a Tableau?

• All variables are set to zero.

• The maximum value is greater than 500.

• All entries in the bottom row are positive.

• There is a negative entry in the left side of the bottom row.

What should be entered if no maximum exists due to an unbounded region?

• N/A

• MAX

• ZERO

• DNE

In the scenario where no maximum exists, what is the reason for this?

• The objective function is too complex.

• The feasible region is unbounded.

• All variables are inactive.

• The Tableau is incomplete.