To determine the basic feasible solution from the given tableau, we need to identify the variables that correspond to identity matrix columns (basic variables) and those that don’t (nonbasic variables).

Here is the tableau given:

Step 1: Identify Basic and Nonbasic Variables

In a basic feasible solution:

• Basic variables have their columns form part of an identity matrix (with a "1" in one row and "0"s elsewhere).
• Nonbasic variables will be set to zero in the solution.

Analyzing the Tableau:

From the tableau:

• $s_1$ and $s_2$ each have a column that closely resembles part of an identity matrix, meaning they are basic variables.
• $x_1$ and $x_2$ do not have columns that resemble part of the identity matrix, making them nonbasic variables.

Therefore:

• Basic variables: $s_1$ and $s_2$
• Nonbasic variables: $x_1$ and $x_2$

Conclusion

The answer is:

$s_1$ and $s_2$ are basic, and $x_1$ and $x_2$ are nonbasic.

Would you like to know more details or have any questions?

1. How to find the basic feasible solution from a simplex tableau?
2. Why are nonbasic variables set to zero in a basic feasible solution?
3. What does the identity matrix represent in a simplex tableau?
4. How to interpret the right-hand side values in this tableau?
5. What role do slack variables play in the simplex method?

Tip: In the simplex method, the basic variables are typically those that can represent constraints in the feasible region, forming a solution that satisfies all constraints.