SAMPLE FINAL EXAM, Management Science (QMIS 205)

PLEASE NOTE: Final Exam is Comprehensive . Students should also review the sample

test for the midterm

True or False questions

1. In LP, the objective function always consists of either maximizing or minimizing some value.

2. Parameters are known, constant values that are usually coefficients of variables in equations.

3. Binary variables are best suited to be the decision variables when dealing with yes-or-no decisions.

4. If a transportation problem has four origins and five destinations, the LP formulation of the problem will

have nine functional (structural) constraints.

5. A transportation problem with 3 sources and 4 destinations will have exactly 7 terms in the objective

function.

6. In an unbalanced transportation model, all constraints are equalities.

7. Assignment problems are cost minimization problems and cannot be solved as a profit maximization

problem.

8. In an assignment problem, every source and every destination has a demand of either 0 or 1.

9. A prohibited route in a transportation model should be assigned an arbitrarily high cost coefficient.

10. A constraint with a ≥ sign in a linear programming model is to restrict the usage of a limited resource.

11. To find the optimal solution for an integer programming problem we can solve it as a linear

programming problem and then round the solution.

12. In LP, an infeasible solution violates all of the constraints of the problem.

13. When solving a minimization problem graphically, it is generally the goal to move the objective

function line out, away from the origin, as far as possible.

14. In a total integer model, all decision variables have integer solution values.

15. In a mixed integer model, some solution values for decision variables are integer and others can be non-integer.

16. When a certain route in a transportation problem does not exist, the problem cannot be formulated as a

transportation problem.

17. When the number of people and the number of tasks are not equal in an assignment problem then the

problem cannot be solved.

18. The president of a company is deciding to choose from among five equally qualified candidates for her

vice-president position. If this situation could be modeled as a linear program, the decision variables

would be binary (0-1).

19. Sensitivity ranges can be computed only for the right-hand sides of constraints.

20. The sensitivity range for an objective function coefficient is the range of values over which the profit

does not change.

21. The sensitivity range for a constraint quantity value is the range over which the shadow price is valid.

Multiple Choice 22. In linear programming, solutions that satisfy all of the constraints simultaneously are referred to as:

a. optimal.

b. feasible.

c. nonnegative.

d. targeted.

e. All of the above.

23. Which objective function has the same slope as this line: 4x + 2y = 20.

a. 2x +4y = 20.

b. 2x – 4y = 20.

c. 4x – 2y = 20.

d. 4x + 2y = 10.

e. None of the above.

24. Given the following 2 constraints, which solution is a feasible solution for a maximization problem?

(1) 14x1 + 6x2 ≤ 42

(2) x1 – x2 ≤ 3

a. (x1, x2 ) = (1,5).

b. (x1, x2 ) = (2,1).

c. (x1, x2 ) = (4,4).

d. (x1, x2 ) = (5,1).

e. (x1, x2 ) = (2,6).

25. The assignment problem constraint x31 + x32 + x33 + x34 < 2 means

a. agent 3 can be assigned to at most 2 tasks.

b. agent 2 can be assigned to at least 3 tasks.

c. agents 1, 2, 3, and 4 will be assigned to task 3.

d. agent 3 will be assigned to at least 2 tasks.

26. Let x1 , x2 , and x3 be binary (0 – 1) variables whose values indicate whether the projects are done (xi=1)

or are not done (xi=0). Which answer below indicates that at least two of the projects must be done?

a. x1 + x2 + x3 > 2

b. x1 + x2 + x3 < 2

c. x1 + x2 + x3 = 2

d. x1 - x2 = 0

27. In linear programming, sensitivity (what-if) analysis is associated with determining the effect of

changing:

I. objective function coefficients.

II. right-hand side values of constraints.

III. decision variable values.

a. I and II

b. II and III

c. I, II, and III

d. I and III

28. In a binary programming problem with 2 alternatives, x1 and x2, the following constraint needs to be

added to the formulation if the 2 alternatives are mutually exclusive and one of them must be chosen:

a. x1 + x2 ≤ 1.

b. x1 + x2 = 1.

c. x1 - x2 ≤ 1.

d. x1 - x2 = 1.

29. In a binary programming problem with 2 alternatives, x1 and x2, the following constraint needs to be

added to the formulation if the 2 alternatives are mutually exclusive and one of them may be chosen:

a. x1 + x2 ≤ 1.

b. x1 + x2 = 1.

c. x1 - x2 ≤ 1.

d. x1 - x2 = 1.

30. The constraint in a transportation problem implies:

a. demand point 1 (customer 1) can demand up to 250 units.

b. destination 1 has maximum possible demand.

c. supply point 1 (supplier 1) cannot supply more than 250 units.

d. customer 1 can get its supplies from 4 suppliers.

e. none of the above.

31. Which of the following is true about a balanced transportation model:

a. all demand constraints are ≥.

b. all constraints are =.

c. all supply constraints are ≤ and all demand constraints are =.

d. all supply constraints are ≥.

e. none of the above.

32. An assignment problem:

a. is a special type of transportation problem.

b. will always have integer solution.

c. has all supplies and demands equal to 1.

d. all the decision variables are either 0 or1.

e. all of the above.

33. In a mathematical model which requires x1 0 and integer, x2 0, and x3 = (0, 1), which of the following would

not be a feasible solution?

a) x1 = 5, x2 = 3, x3 = 0

b) x1 = 4, x2 = .389, x3 = 1

c) x1 = 2, x2 = 3, x3 = .578

d) x1 = 0, x2 = 8, x3 = 0

34. The graph of a problem that requires x1 and x2 to be integer has a feasible region

a) the same as its LP relaxation.

b) of dots.

c) of horizontal stripes.

d) of vertical stripes.

35. In an all-integer linear programming model,

a) all objective function coefficients must be integer.

b) all right-hand side values must be integer.

c) all variables must be integer.

d) all objective function coefficients and right-hand side values must be integer.

Questions 35 to 41 refer to the following problem:

The production planner for Fine Coffees, Inc. produces two coffee blends: American (A) and British (B).

He can only get 300 pounds of Colombian beans per week and 200 pounds of Dominican beans per

week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of

Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for

the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound.

NOTE: One Pound = 16 ounces (i.e., there are 16 ounces in a pound)

36. What is the objective function?

a. P = A + 2B.

b. P = 12A + 8B.

c. P = 2A + B.

d. P = 8A + 12B.

e. P = 4A + 8B.

37. What is the constraint for Colombian beans?

a. A + 2B ≤ 4,800.

b. 12A + 8B ≤ 4,800.

c. 2A + B ≤ 4,800.

d. 8A + 12B ≤ 4,800.

e. 4A + 8B ≤ 4,800.

38. What is the constraint for Dominican beans?

a. 12A + 8B ≤ 4,800.

b. 8A + 12B ≤ 4,800.

c. 4A + 8B ≤ 3,200.

d. 8A + 4B ≤ 3,200.

e. 4A + 8B ≤ 4,800.

39. Which of the following is not a feasible solution?

a. (A, B) = (0, 0).

b. (A, B) = (0, 400).

c. (A, B) = (200, 300).

d. (A, B) = (400, 0).

e. (A, B) = (400, 400).

40. A new constraint is added to the above problem that states "due to insufficient demand, the weekly

production of the American blend should not exceed 800 ounces. Adding this new requirement to the

above problem will result in which of the following?

a. There will be a new optimal solution

b. There will be an increase in the production of the British blend

c. The optimal solution will remain the same

d. There will be a decrease in the production of the British blend

e. none of the above.

41. Once more, referring to the original problem above, a new constraint is added that states "due to the

popularity of the American blend, the weekly production of the American blend should be at least 800

ounces. Adding this new requirement to the above problem will result in which of the following?

a. There will be a new optimal solution

b. There will be an increase in the production of the American blend

c. There is no feasible solution

d. There will be a decrease in the production of the British blend

e. b and d.

Consider a transportation problem where there are 2 suppliers and 3 customers. The table below presents

the supply, demand and transportation costs from each source to each destination. Let Xij represent the

number of shipments from source i to destination j.

Destination

Source

1 2 3 Supply

1 5 4 9 300

2 8 3 7 500

Demand 200 350 250

42. The objective function for this transportation problem is:

a) Max 5X11 + 4X12 + 9X13 +8X21 + 3X22 + 7X23

b) Min 5X11 + 4X12 + 9X13 +8X21 + 3X22 + 7X23

c) Max X11 + X12 + X13 +X21 + X22 + X23

d) Min X11 + X12 + X13 +X21 + X22 + X23

e) None of the above

43. What is the supply constraint for source 2?

a) 8X21 + 3X22 + 7X13 ≤ 500

b) X11 + X12 + X13 +X21 + 3X22 + 7X23 ≤ 500

c) X21 + X22 + X23 = 500

d) X21 + X22 + X23 ≤ 500

e) X21 + X22 + X23 ≥ 500

44. What is the demand constraint for destination 3?

a) 9X13 + 7X23 ≤ 250

b) X11 + X12 + X13 +X21 + 3X22 + 7X23 = 250

c) X13 + X23 = 250

d) X13 + X23 + X33 = 250

e) X31 + X32 + X33 ≥ 250

Spread Sheet Modeling

Questions 1 through 4 in this part refer to the following spreadsheet model for a cost minimization problem.

1 Where are the data cells located?

a. B2:C2, B5:C7, and F5:F7.

b. B2:C2.

c. B10:C10.

d. F10.

e. None of the above.

2 Where are the changing cells located?

a. B10:C10.

b. B2:C2, B5:C7, and F5:F7.

c. B2:C2.

d. F10.

e. None of the above.

123456789

10

A B C D E F

Activity 1 Activity 2Unit Cost $15 $20

Benefit Totals Needed

A 1 2 10 >= 10B 2 3 16 >= 6C 1 1 6 >= 6

Activity 1 Activity 2 Total Cost

Solution 2 4 $110

Contribution per Unit

3 Where is the target cell located?

a. B2:C2.

b. B2:C2, B5:C7, and F5:F7.

c. F10

d. B10:C10.

e. None of the above.

4 Where are the output cells located?

a. B2:C2.

b. B2:C2, B5:C7, and F5:F7.

c. B10:C10.

d. F10.

e. None of the above.

5 Where are the decision variables located?

a. B10:C10.

b. B2:C2, B5:C7, and F5:F7.

c. B2:C2.

d. F10.

e. None of the above.

6 If the optimal solution remains the same but the unit cost for activity 1 increases to 25, then the new

total cost would be:

a. 130

b. 50

c. 100

d. will be the same as before.

e. None of the above.

7 If the optimal solution remains the same but the unit cost for activity 2 increases by 10, then the new

total cost would be:

a. 150

b. 50

c. 130

d. will be the same as before.

e. None of the above.