# St. leo decisions 550 – 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

is already

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

B iPad covers with MBA logo $25/unit Not needed unless we buy iPads

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

B iPad covers with MBA logo $25/unit Not needed unless we buy iPads

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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