A basic feasible solution is a solution to an LP problem that corresponds to a corner point of the feasible region.

1. True

2. False

In preparing $\text{≥}$ constraint for an initial simplex tableau, you would

1. add a slack variable.

2. add a surplus variable.

3. subtract an artificial variable.

4. subtract a surplus variable and add an artificial variable.

In the initial simplex tableau, the solution mix variables can be

1. only slack variables.

2. slack and surplus variables.

3. artificial and surplus variables.

4. slack and artificial variables.

Even if an LP problem involves many variables, an optimal solution will always be found at a corner point of the n-dimensional polyhedron forming the feasible region.

1. True

2. False

Which of the following in a simplex tableau indicates that an optimal solution for a maximization problem has been found?

1. All the $C_j-Z_j$ values are negative or zero.

2. All the $C_j-Z_j$ values are positive or zero.

3. All the substitution rates in the pivot column are negative or zero.

4. There are no more slack variables in the solution mix.

To formulate a problem for solution by the simplex method, we must add slack variables to

1. all inequality constraints.

2. only equality constraints.

3. only “greater than” constraints.

4. only “less than” constraints.

If in the optimal tableau of an LP problem an artificial variable is present in the solution mix, this implies

1. infeasibility.

2. unboundedness.

3. degeneracy.

4. alternate optimal solutions.

If in the final optimal simplex tableau the $C_j-Z_j$ value for a nonbasic variable is zero, this implies

1. feasibility.

2. unboundedness.

3. degeneracy.

4. alternate optimal solutions.

In a simplex tableau, all of the substitution rates in the pivot column are negative. This indicates that

1. there is no feasible solution to this problem.

2. the solution is unbounded.

3. there is more than one optimal solution.

4. the solution is degenerate.

The pivot column in a maximization problem is the column with

1. the greatest positive $C_j-Z_j.$

2. the greatest negative $C_j-Z_j.$

3. the greatest positive $Z_j.$

4. the greatest negative $Z_j.$

A change in the objective function coefficient $\left(C_j\right)$ for a basic variable can affect

1. the $C_j-Z_j$ values of all the nonbasic variables.

2. the $C_j-Z_j$ values of all the basic variables.

3. only the $C_j-Z_j$ value of that variable.

4. the $C_j$ values of other basic variables.

Linear programming has few applications in the real world due to the assumption of certainty in the data and relationships of a problem.

1. True

2. False

In a simplex tableau, one variable will leave the basis and be replaced by another variable. The leaving variable is

1. the basic variable with the largest $C_j.$

2. the basic variable with the smallest $C_j.$

3. the basic variable in the pivot row.

4. the basic variable in the pivot column.

Which of the following must equal 0?

1. basic variables

2. solution mix variables

3. nonbasic variables

4. objective function coefficients for artificial variables

The shadow price for a constraint is

1. the value of an additional unit of that resource.

2. always equal to zero if there is positive slack for that constraint.

3. found from the $C_j-Z_j$ value in the slack variable column.

4. all of the above.

The solution to the dual LP problem

1. presents the marginal profit of each additional unit of resource.

2. can always be derived by examining the $Z_j$ row of the primal’s optimal simplex tableau.

3. is better than the solution to the primal.

4. is all of the above.

The number of constraints in a dual problem will equal the number of

1. constraints in the primal problem.

2. variables in the primal problem.

3. variables plus the number of constraints in the primal problem.

4. variables in the dual problem.