Deck 17: LP: Simplex Method

Question 1

To determine a basic solution set of n-m, the variables equal to zero and solve the m linear constraint equations for the remaining m variables.

Answer 1

True

Question 2

A basic feasible solution satisfies the nonnegativity restriction.

Answer 2

True

Question 3

Which of the following is not a step that is necessary to prepare a linear programming problem for solution using the simplex method?

A)formulate the problem.
B)set up the standard form by adding slack and/or subtracting surplus variables.
C)perform elementary row and column operations
D)set up the tableau form

Answer 3

C

Question 4

What coefficient is assigned to an artificial variable in the objective function?

A)zero.
B)one.
C)a very large negative number.
D)a very large positive number.

Question 5

When there is a tie between two or more variables for removal from the simplex tableau,

A)post-optimality analysis is required.
B)their dual prices will be equal.
C)converting the pivot element will break the tie.
D)a condition of degeneracy is present.

Question 6

Algebraic methods such as the simplex method are used to solve

A)nonlinear programming problems.
B)any size linear programming problem.
C)programming problems under uncertainty.
D)graphical models.

Question 7

When a system of simultaneous equations has more variables than equations, there is a unique solution.

Question 8

When a set of simultaneous equations has more variables than constraints,

A)it is a basic set.
B)it is a feasible set.
C)there is a unique solution.
D)there are many solutions.

Question 9

In a simplex tableau, there is a variable associated with each column and both a constraint and a basic variable associated with each row.

Question 10

Which is not required for a problem to be in tableau form?

A)Each constraint must be written as an equation.
B)Each of the original decision variables must have a coefficient of 1 in one equation and 0 in every other equation.
C)There is exactly one basic variable in each constraint.
D)The right-hand side of each constraint must be nonnegative.

Question 11

The purpose of the tableau form is to provide

A)infeasible solution.
B)optimal infeasible solution.
C)initial basic feasible solution.
D)degenerate solution.

Question 12

The values in the c_j - z_j , or net evaluation, row indicate

A)the value of the objective function.
B)the decrease in value of the objective function that will result if one unit of the variable corresponding to the jth column of the A matrix is brought into the basis.
C)the net change in the value of the objective function that will result if one unit of the variable corresponding to the jth column of the A matrix is brought into the basis.
D)the values of the decision variables.

Question 13

An alternative optimal solution is indicated when in the simplex tableau

A)a non-basic variable has a value of zero in the c_j - z_j row.
B)a basic variable has a positive value in the c_j - z_j row.
C)a basic variable has a value of zero in the c_j - z_j row.
D)a non-basic variable has a positive value in the c_j - z_j row.

Question 14

A basic solution and a basic feasible solution

A)are the same thing.
B)differ in the number of variables allowed to be zero.
C)describe interior points and exterior points, respectively.
D)differ in their inclusion of nonnegativity restrictions.

Question 15

A minimization problem with four decision variables, two greater-than-or-equal-to constraints, and one equality constraint will have

A)2 surplus variables, 3 artificial variables, and 3 variables in the basis.
B)4 surplus variables, 2 artificial variables, and 4 variables in the basis.
C)3 surplus variables, 3 artificial variables, and 4 variables in the basis.
D)2 surplus variables, 2 artificial variables, and 3 variables in the basis.

Question 16

Infeasibility exists when one or more of the artificial variables

A)remain in the final solution as a negative value.
B)remain in the final solution as a positive value.
C)have been removed from the basis.
D)remain in the basis.

Question 17

At each iteration of the simplex procedure, a new variable becomes basic and a currently basic variable becomes nonbasic, preserving the same number of basic variables and improving the value of the objective function.

Question 18

In the simplex method, a tableau is optimal only if all the c_j - z_j values are

A)zero or negative.
B)zero.
C)negative and nonzero.
D)positive and nonzero.

Question 19

Unit columns are used to identify

A)the tableau.
B)the c row.
C)the b column.
D)the basic variables.

Question 20

Every extreme point of the graph of a two variable linear programming problem is a basic feasible solution.

Question 21

We recognize infeasibility when one or more of the artificial variables do not remain in the solution at a positive value.

Question 22

Coefficients in a nonbasic column in a simplex tableau indicate the amount of decrease in the current basic variables when the value of the nonbasic variable is increased from 0 to 1.

Question 23

The variable to enter into the basis is the variable with the largest positive c_j - z_j value.

Question 24

Artificial variables are added for the purpose of obtaining an initial basic feasible solution.

Question 25

The purpose of row operations is to create a unit column for the entering variable while maintaining unit columns for the remaining basic variables.

Question 26

The coefficient of an artificial variable in the objective function is zero.

Question 27

The variable to remove from the current basis is the variable with the smallest positive c_j - z_j value.

Question 28

A solution is optimal when all values in the c_j - z_j row of the simplex tableau are either zero or positive.

Question 29

If a variable is not in the basis, its value is 0.