Simplex Method Concepts and Applications

What is a standard maximization problem in the context of the simplex method?

• A problem with only one variable.

• A problem where all variables are non-negative and constraints are less than or equal to a non-negative number.

• A problem with no constraints.

• A problem where all variables are negative.

What are active variables in the simplex method?

• Variables that are always zero.

• Variables corresponding to columns with only one and non-zero entries.

• Variables that are always negative.

• Variables that are not used in the tableau.

What is the purpose of introducing slack variables in the simplex method?

• To convert inequalities into equations.

• To eliminate variables from the problem.

• To reduce the number of constraints.

• To make the problem more complex.

How is the initial tableau set up in the simplex method?

• By listing all variables and their coefficients from the equations.

• By using only the constraints.

• By ignoring the slack variables.

• By using only the objective function.

What determines the pivot column in the simplex method?

• The column with the most positive number in the bottom row.

• The column with the smallest number in the top row.

• The column with the most negative number in the bottom row.

• The column with the largest number in the top row.

How do you determine the pivot row in the simplex method?

• By dividing each entry in the constant column by the corresponding positive entry in the pivot column and choosing the smallest ratio.

• By selecting the row with the smallest number.

• By choosing the row with the most negative number.

• By selecting the row with the largest number.

What is the goal of performing row operations in the simplex method?

• To increase the number of variables.

• To make the pivot equal to one and other elements in the pivot column zero.

• To eliminate the objective function.

• To make all entries in the tableau zero.

When is the solution found in the simplex method?

• When the pivot column is zero.

• When the tableau has no active variables.

• When the left side of the last row is all non-negative.

• When all entries in the tableau are negative.

How does the simplex method compare to graphical methods?

• It is less accurate than graphical methods.

• It only works for problems with one variable.

• It moves along the edges of the polytope to find the optimal solution, similar to graphical methods.

• It does not require any constraints.

What is the final step in the simplex method?

• To eliminate all variables.

• To interpret the final tableau and determine the solution.

• To repeat the process until all entries are negative.

• To graph the solution.