Multiple Choice
Identify the
choice that best completes the statement or answers the question.
|
|
|
1.
|
Dual prices and ranges for objective function coefficients and right-hand side
values are found by considering
a. | dual analysis. | b. | optimality analysis. | c. | ranging
analysis. | d. | sensitivity analysis. |
|
|
|
2.
|
For the basic feasible solution to remain optimal
a. | all cj - zj values must remain £ 0. | b. | no objective function coefficients are allowed
to change. | c. | the value of the objective function must not change. | d. | each of the above is
true. |
|
|
|
3.
|
A one-sided range of optimality
a. | always occurs for non-basic variables. | b. | always occurs for basic
variables. | c. | indicates changes in more than one coefficient. | d. | indicates changes in
a slack variable's coefficient. |
|
|
|
4.
|
A linear programming problem with the objective function 3x1 +
8x2 has the optimal solution x1 = 5, x2 = 6. If c2
decreases by 2 and the range of optimality shows 5 £ c2
£ 12, the value of Z
a. | will decrease by 12. | b. | will decrease by 2. | c. | will not
change. | d. | cannot be determined from this information. |
|
|
|
5.
|
The improvement in the value of the optimal solution per-unit increase in a
constraint's right-hand side is
a. | the slack value. | b. | the dual price. | c. | never
negative. | d. | the 100% rule. |
|
|
|
6.
|
The dual variable represents
a. | the marginal value of the constraint | b. | the right-hand side value of the
constraint | c. | the artificial variable | d. | the technical coefficient of the
constraint |
|
|
|
7.
|
The range of feasibility indicates right-hand side values for which
a. | the value of the objective function will not change. | b. | the values of the
decision variables will not change. | c. | those variables which are in the basis will not
change. | d. | more simplex iterations must be performed. |
|
|
|
8.
|
If the dual price for b1 is 2.7, the range of feasibility is 20 £ b1 £ 50, and the original
value of b1 was 30, which of the following is true?
a. | There currently is no slack in the first constraint. | b. | We would be willing
to pay up to €2.70 per unit for up to 20 more units of resource 1. | c. | If only 25 units of
resource 1 were available, profit would drop by €13.50. | d. | Each of the above is
true. |
|
|
|
9.
|
The number of constraints to the dual of the following problem is: | Max Z | = 3x1 + 2x2
+ 6x3 | | | | | s.t. | 4x1 + 2x2 + 3x3 ³ 100 | | | 2x1 + x2 - 2x3 £
200 | | | 4x2 + x3 ³
200 | | |
|
|
|
10.
|
Given the simplex tableau for the optimal primal solution
a. | the values of the dual variables can be found from the cj - zj values of the slack/surplus variable
columns. | b. | the values of the dual surplus variables can be found from the cj - zj values of the primal decision variable
columns. | c. | the value of the dual objective function will be the same as the objective function
value for the primal problem. | d. | each of the above is
true. |
|