# If the solution values of a linear program

Question
1. If the solution values of a linear program are rounded in order to obtain an integer solution, the solution is: (Points : 5)
always optimal and feasible.
sometimes optimal and feasible.
always feasible.
never optimal and feasible.
Question 2. 2. A PERT/CPM activity has an optimistic time estimate of 3 days, a most likely time estimate of 8 days, and a pessimistic time estimate of 10 days. The expected time (in days) of this activity is ____. (Points : 5)
7.0
7.5
8.0
8.5
Question 3. 3. The critical path is the ________ path through the network. (Points : 5)
longest
shortest
straightest
most expensive
Question 4. 4. For most graphs, the constraint equations which intersect to form a solution point must be solved simultaneously: (Points : 5)
because the solution coordinates from the graph cannot be visually read with high precision.
in order to confirm the mathematically determined coordinates.
in order to determine all of the optimal point solution.
because the slope b and the y-intercept a are not always integers.
Question 5. 5. Cully Turniture buys two products for resale: big shelves (B) and medium shelves (M). Each big shelf costs \$500 and requires 100 cubic feet of storage space, and each medium shelf costs \$300 and requires 90 cubic feet of storage space. The company has \$75,000 to invest in shelves this week, and the warehouse has 18,000 cubic feet available for storage. Profit for each big shelf is \$300 and for each medium shelf is \$150. What is the storage space constraint? (Points : 5)
90 B + 100 M = 18000
90 B + 100 M = 18000
100 B + 90 M = 18000
500 B + 300 M = 18000
Question 6. 6. In a 0-1 integer programming model, if the constraint x1 – x2 = 0, it means when project 2 is selected, project 1 ________ be selected. (Points : 5)
must always
can sometimes
can never
Question 7. 7. Which of the following is not an integer linear programming problem? (Points : 5)
Pure integer
Mixed integer
0-1 integer
Continuous
Question 8. 8. The \$75 per credit hour course fee tacked on to all the MBA classes has generated a windfall of \$56,250 in its first semester. “Now we just need to make sure we spend it all,” the Assistant Dean cackled. She charged the Graduate Curriculum Committee with generating a shopping list before their next meeting. Four months later, the chairman of the committee distributed the following. As the professor for the quantitative modeling course, he tended to think in terms of decision variables, so he added the left-most column for ease of use.
Decision
Variable Item Cost Note
A iPads for everybody \$750/unit Must get a cover if these are purchased
C Speaker series \$15,000 Can’t afford both this and the iPads
D Subscriptions to the Wall
Street Journal \$10/unit Don’t need if we have the electronic version
E Subscriptions to the electronic
version of the Wall Street
Journal \$5/unit Worthless without the iPads
Which constraint best describes the situation with decision variables A and B? (Points : 5)
B – A = 0
B + A = 0
B + A = 1
B – A = 1
Question 9. 9. Non-negativity constraints: (Points : 5)
require the use of greater-than-or-equal-to constraints.
restrict the decision variables to positive values.
restrict the decision variables to negative values.
do not restrict the sign of the decision variable.
Question 10. 10. Which of the following could be a linear programming objective function? (Points : 5)
Z = 1A + 2BC + 3D
Z = 1A + 2B + 3C + 4D
Z = 1A + 2B / C + 3D
Z = 1A + 2B2 + 3D
Question 11. 11. A graphical solution is limited to linear programming problems with: (Points : 5)
1 decision variable.
2 decision variables.
3 decision variables.
4 decision variables.
Question 12. 12. The term refers to testing how a problem solution reacts to changes in one or more of the model parameters. (Points : 5)
Priority recognition
Decision analysis
Analysis of variance
Sensitivity analysis
Question 13. 13. Which of the list of items below is not a component of a linear programming problem? (Points : 5)
Constraints
Objective function
Decision variables
Nonlinear residual
Question 14. 14. Types of integer programming models are ________. (Points : 5)
total
0-1
mixed
all of the above
Question 15. 15. If we are solving a 0-1 integer programming problem, the constraint x1 + x2 = 1 is a ________ constraint. (Points : 5)
multiple-choice
mutually exclusive
conditional
corequisite
Question 16. 16. The \$75 per credit hour course fee tacked on to all the MBA classes has generated a windfall of \$56,250 in its first semester.“Now we just need to make sure we spend it all,” the Assistant Dean cackled. She charged the Graduate Curriculum Committee with generating a shopping list before their next meeting. Four months later, the chairman of the committee distributed the following. As the professor for the quantitative modeling course, he tended to think in terms of decision variables, so he added the left-most column for ease of use.
Decision
Variable Item Cost Note
A iPads for everybody \$750/unit Must get a cover if these are purchased
C Speaker series \$15,000 Can’t afford both this and the iPads
D Subscriptions to the Wall
Street Journal \$10/unit Don’t need if we have the electronic version
E Subscriptions to the electronic
version of the Wall Street
Journal \$5/unit Worthless without the iPads
Which of the following constraints best describes the relationship between the electronic Wall Street Journal subscription and the iPads? (Points : 5)
E + A = 0
E + A = 1
E – A ≤ 0
E – A ≤ 1
Question 17. 17. A work breakdown structure breaks down a project into: (Points : 5)
weeks.
areas.
arcs.
modules.
Question 18. 18. Cully Furniture buys two products for resale: big shelves (B) and medium shelves (M). Each big shelf costs \$500 and requires 100 cubic feet of storage space, and each medium shelf costs \$300 and requires 90 cubic feet of storage space. The company has \$75,000 to invest in shelves this week, and the warehouse has 18,000 cubic feet available for storage. Profit for each big shelf is \$300 and for each medium shelf is \$150. If the furniture company purchases no big shelves and 200 medium shelves, which of the two resources will be completely used (at capacity)? (Points : 5)
Investment money only
Storage space only
Investment money and storage space
Neither investment money nor storage space
Question 19. 19. A linear programming model consists of: (Points : 5)
decision variables.
an objective function.
constraints.
all of the above
Question 20. 20. If a maximization linear programming problem consists of all less-than-or-equal-to constraints with all positive coefficients and the objective function consists of all positive objective function coefficients, then rounding down the linear programming optimal solution values of the decision variables will ________ result in a(n) ________ solution to the integer linear programming problem. (Points : 5)
always; optimal
always; non-optimal
never; non-optimal
sometimes; optimal

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