Mastering the Simplex Method

What is the primary goal of the simplex method?

• To identify all feasible solutions to a linear programming problem.

• To convert a linear programming problem into a quadratic one.

• To find the optimal solution to a linear programming problem.

• To minimize the number of variables in a linear programming problem.

In the context of the simplex method, what is a feasible solution?

• A solution that is not defined in the problem space.

• A solution that violates at least one constraint.

• A solution that meets all constraints of the linear programming problem.

• A solution that maximizes the objective function only.

Which of the following represents a basic variable in a simplex tableau?

• Basic variables are represented by the non-basic columns in the tableau.

• Basic variables are represented by the columns of the identity matrix in the simplex tableau.

• Basic variables are represented by the rows of the identity matrix.

• Basic variables are the constants in the objective function.

What does a pivot operation in the simplex method involve?

• Selecting a pivot element and updating the tableau.

• Eliminating all non-basic variables from the tableau.

• Calculating the objective function without any adjustments.

• Choosing a random element without updating the tableau.

How can you identify an optimal solution in a simplex tableau?

• An optimal solution is identified when all coefficients in the objective function row are non-negative.

• An optimal solution is identified when all coefficients in the objective function row are negative.

• An optimal solution is found when the solution is feasible but not bounded.

• An optimal solution is determined by the highest value in the constraint rows.

What does it mean if a tableau has a negative indicator in the objective row?

• The objective function is maximized.

• The solution is optimal and cannot be improved.

• The current solution is not optimal.

• The tableau is infeasible and has no solution.

Which of the following is true about the basic feasible solution?

• A basic feasible solution is always unique.

• A basic feasible solution does not need to satisfy all constraints.

• A basic feasible solution can have negative variable values.

• A basic feasible solution satisfies all constraints and has non-negative variable values.

What is the significance of the entering variable in the simplex method?

• The entering variable indicates which variable will decrease to improve the objective function.

• The entering variable is used to identify the basic feasible solution.

• The entering variable determines the optimal solution directly.

• The entering variable indicates which variable will increase to improve the objective function.

How do you determine the leaving variable during a pivot operation?

• Select the variable with the smallest coefficient in the constraint equations.

• Identify the variable with the highest value in the current solution.

• Identify the basic variable with the largest positive or negative coefficient in the objective function row.

• Choose any non-basic variable at random.

What is the result of performing a pivot operation in the simplex tableau?

• The tableau is discarded after the operation.

• The variables are all set to zero.

• The tableau is updated to reflect a new basic feasible solution.

• The objective function is minimized immediately.