S.No Question

1 Which of the following is a component of a linear programming model?

a. Constraints

b. Decision variables

c. Objective Function

d. All of the above.

2 Which of the following is not a type of cell in a linear programming spreadsheet model?

a. Input cells.

b. Target cell

c. Output cells

d. Data cells.

3 The cell containing the measure of performance is referred to as:

a. Changing cell

b. Target cell

c. Output cells.

d. Data cells

4For the products x and y, which of the following could be a linear programming objective function?

a. C = x + 2y.

b. C = x – 2y2

c. C = x + 2x/y.

d. All of the above.

5 Which of the following is not a step in the graphical method

a. Draw the constraint boundary line for each functional constraint

b. Find the feasible region

c. Find the optimal solution using a straight-edge

d. Use Excel Solver

6

Given the following two constraints, which solution is a feasible solution for a maximization

problem?

Constraint 1 : 4 X1 + 3 X2 ≤ 18,

Constraint 2: X1 – X2 ≤ 3

a. (X1, X2 ) = (1, 5).

b. (X1, X2 ) = (4, 1).

c. (X1, X2 ) = (4, 0).

d. (X1, X2 ) = (2, 1).

7 Sensitivity analysis is used for the following purpose

a.To check the effect on the recommendations of a model if the estimates turn out to be wrong

b. To check if the solution is correct

c. It is only used for the graphical solution

d. None of the above

8If the availability of an additional unit of a resource has any effect on the Objective Function, then

that constraint is said to be

a. A Binding Constraint

b. A Non-Binding Constraint

c. A Functional Constraint

d. A Given Constraint

9 Which of the following is not a component of a mathematical model for decision making?

a. Decision variables.

b. A spreadsheet

c. Constraints

d. Parameters

10 A constraint in a mathematical model is

a. A variable representing the decision to be made

b. An inequality or equation that restricts the values of the decision variables.

c. A measure of the performance of the model

d. The sales forecast.

11 Which of the following may not be in a linear programming formulation?

a. <=

b. >

c. =

d. a. and c. only

12 A linear programming model is characterized by

a. Continuous variables that can assume any value

b. Integer variables only

c. Binary integers only

d. All of the above

13If the right-hand side value of a constraint in a two variable linear programming problems is

changed, then

a. The optimal measure of performance may change

b. A parallel shift must be made in the graph of that constraint

c. The optimal values for one or more of the decision variables may change

d. All of the above

14 Which if the following is true for Shadow Price

a.A shadow price indicates how much the optimal value of the objective function will decrease per

unit decrease in the right-hand side of a constraint

b.Shadow price is associated with the functional constraint (Left Hand Side of a Constraint)

c. Shadow price is only linked to the decision variables

d. All above statements are true

15 In a Binary Integer Programming Problem, Binary variables can have the following values

a. 0

b. 1

c. Any integer value

d. a. and b. only

16Which of the following is a probable reason for choosing simulation as a decision-making tool?

a. The situation is too complex for a mathematical model

b. Users are able to understand the model

c. There is a limited time in which to obtain results

d. a. and b. only

17 Which of the following is considered to be a main advantage of simulation?

a. It permits experimentation with the system.

b. It generates an optimum solution.

c. It compresses time

d. a. and c. only

18

In a BIP problem, 1 corresponds to a yes decision and 0 to a no decision. If there are 3 projects

under consideration (A, B, and C) and at most 2 can be chosen then the following constraint needs

to be added to the formulation

a. A + B + C <= 2

b. A + B + C >= 2

c. A + B + C = 2

d. None of the above

19The part of a linear programming model that expresses what needs to be either maximized or

minimized depending upon the objective of the problem is called

a. Objective Function

b. Constraint

c. A Feasible Solution

d. None of the above

20 Which of the following is true at the break-even point?

a. The fixed cost equals the variable cost

b. The production quantity equals the sales forecast

c. The company will neither make nor lose money on the product

d. The profit equals the cost

21 Enlightened future managers do not need to know which of the following?

a. When management science can and cannot be applied.

b. How to apply the major techniques of management science.

c. How to interpret the results of a management science study.

d. The mathematical theory behind the techniques of management science

22 Which of the following is not a category of linear programming problems?

a. Resource-allocation problems

b. Cost-benefit-tradeoff problems.

c. Transportation problems

d. All of the above are categories of linear programming problems

23 Pure Transportation problems have the following type of constraints

a. >=

b. <=

c. >

d. None of the above

24 Resource-allocation problems typically have which of the following type of constraints

a. >= (Benefit Constraint)

b. <= (Resource Constraint)

c. = (Fixed Requirement Constraint)

d. All of the above

25 Good Excel modeling practice includes the following

a. Shading cells to differentiate types of cells

b. Use relative and absolute referencing to copy formulas

c. Use Range Names

d. All of the above

26 Cost-benefit tradeoff problems typically have which of the following type of constraints

a. >= (Benefit Constraint)

b. <= (Resource Constraint)

c. = (Fixed Requirement Constraint)

d. All of the above

27 Mixed problems may have which of the following type of constraints

a. >= (Benefit Constraint)

b. <= (Resource Constraint)

c. = (Fixed Requirement Constraint)

d. All of the above

28 Which of the following is an assumption of assignment problems?

a. The number of assignees and the number of tasks are the same

b. The objective is to minimize the number of assignments not made

c. Each task is to be performed by exactly one assignee

d. a. and c. only

29 A coefficient in the objective function is said to be sensitive if

a. Even a small change in its value can change the optimal solution

b. A large change in its value is needed to change the optimal solution

c. Its shadow price is small

d. b. and c. only

30 What-if analysis:

a. May be done graphically for problems with two decision variables

b. May involve changes in the right-hand side values

c. May increase a manager's confidence in the model that has been formulated

d. All of the above

31 Which of the following is not a benefit of what-if analysis

a. It pinpoints the sensitive parameters of the model

b. It gives the new optimal solution if conditions change after a study has been completed

c. It tells management what policy decisions to make

d. b. and c. only

32 Which of the following statements is correct when making decisions?

a. The sum of the state of nature probabilities must be 1

b. Every probability must be greater than or equal to 0

c. All probabilities are assumed to be equal

d. a. and b. only.

33 Following is not a feature of Bayes’ Decision Rule

a. It accounts for all the states of nature and their probabilities

b.The expected payoff can be interpreted as what the average payoff would become if the same

situation were repeated many times

c. Bayes’ decision rule directly uses the prior probabilities

d. Always fixed and uniform values are assigned to the prior probabilities

34 Which is considered to be a major advantage of using Bayes’ Decision Rule?

a.There usually is considerable uncertainty involved in assigning values to the prior probabilities

b. It accounts for all the states of nature and their probabilities

c. Prior probabilities inherently are at least largely subjective in nature

d.By focusing on average outcomes, expected (monetary) payoffs ignore the effect that the amount

of variability in the possible outcomes should have on decision making

35

The objective function of a linear programming model is given as:

Maximize Z = x1 + 2 x2

Subject to

Constraint 1: x1 + x2 ≤5, Constraint 2: x1 + 3 x2 ≤9

What is the objective function value if (x1, x2) = (1,1) is used as a possible solution.

a. 3

b. 5

c. 7

d. None of the above

36

Following is an infeasible solution for the linear programming model given below::

Maximize Z = x1 + 2 x2

Subject to

Constraint 1: x1 + x2 ≤5, Constraint 2: x1 + 3 x2 ≤9

a. (x1, x2) = (1,3)

b. (x1, x2) = (3,1)

c. (x1, x2) = (1,1)

d. None of the above

37Which if the following statement is not true for a graphical solution to a linear programming model:

a.In a minimization problem, the optimal solution improves if the objective function line is brought

closer to the origin

b.A graphical solution method can solve any linear programing problem without any restrictions on

the number of decision variables involved

c.In a maximization problem, the value of objective function improves as we move away from origin.

d. None of the above

38 The decision variables are constrained to take only positive values by the following

a. Non Negativity Constraints

b. Functional Constraints

c. Right Hand Side of all constraints

d. All of the above

39For a following minimization problem shown in a graph, the objective function is given by P = Y +

2X, What is the optimal solution

a. (X,Y) = (0,9)

b. (X,Y) = (8,3)

c. (X,Y) = (4,3)

d. (X,Y) = (15,5)

40

For a product-mix maximization problem shown in a graph below, the objective function is given by

P = 300 D+500 W where D and W are the production rates for doors and windows respectively.

What is the optimal solution?

a. (D,W) = (0,6)

b. (D,W) = (2,6)

c. (D,W) = (4,3)

d. (D,W) = (4,0)

41 When solving a maximization problem graphically, the goal is:

a. To move the objective function line in, toward the origin, as far as possible

b. The goal is to move the objective function line away from the origin

c. The constraints are defined by greater than or equal to (≥) signs

d. None of the above

42Following is true when solving a minimization problem graphically to find optimal solutions

a. The goal is to move the objective function line in, toward the origin, as far as possible

b. The goal is to move the objective function line away from the origin

c. The constraints are defined by less than or equal to (≤) signs

d. None of the above

43 Which of the following is not a step taken in a typical management science study?

a. Define the problem and gather data

b. Formulate a model

c. Apply the model and develop recommendations

d. All of the above are typical steps in a management science study

44 Which of the following is not a major step in the process of modeling with spreadsheets

a. Plan

b. Build

c. Test

d. All of the above.

45 Which of the following are useful steps in the planning stage?

a. Visualize where you want to finish

b. Do some calculations by hand

c. Sketch out a spreadsheet

d. All of the above.

46A linear programming mathmatical model does not contain which of the following components

a. Data.

b. Decisions

c. Constraints

d. A spreadsheet

47 The following statement is true:

a.The optimal measure of performance may change if the right-hand side value of a constraint in a

two variable linear programming problems is changed.

b.A parallel shift must be made in the graph of that constraint if the right-hand side value of a

constraint in a two variable linear programming problems is changed.

c.The optimal values for one or more of the decision variables may change if the right-hand side

value of a constraint in a two variable linear programming problems is changed

d. All of the above are true statements

48 The Following statement is true

a.A coefficient in the objective function is said to be sensitive if even a small change in its value can

change the optimal solution

b.A coefficient in the objective function is said to be sensitive if A large change in its value is needed

to change the optimal solution

c.A coefficient in the objective function is said to be sensitive if its shadow price is small.

d. All of the above statements are true

49 In a problem with 2 decision variables, the 100% rule indicates that each coefficient can be safely

increased by __________________ without invalidating the current optimal solution?

a. 50%

b. 50% of the allowable increase of that coefficient

c. 100%

d. 50% of the range of optimality

50

A linear programming model given below:

Maximize Z = x1 + 2 x2

Subject to

Constraint 1: x1 + x2 ≤5, Constraint 2: x1 + 3 x2 ≤9.

What is the objective function value if (x1, x2) = (3,1) is used as a possible solution?

a. 4

b. 5

c. 7

d. None of the above