S.No Question 1 Which Which of the followi following ng is a componen componentt of a linear linear programm programming ing model? model? a. Constraints
b. c. d. 2 a. b. c. d. 3 a. b. c. d.
4
Deci Decisi sion on vari variab able less Objective Function All of the above. Which of the following is not a type of cell in a linear programming spreadsheet model? Inp Input cell cellss. Target cell
Outpu tput cel cells Data Data cell cellss. The cell cell contain containing ing the the measure measure of perfor performanc mance e is referred referred to as: Chan Changi ging ng cell cell T ar ar ge get ce cell Outpu tput cel cells ls.. Data c el ells For the products x and y, which of the following could be a linear programming objective function?
a.
C = x + 2 y.
b.
C = x – 2y
c. d. 5 a. b. c. d.
C = x + 2x/y. All All of of the the abov above. e. Which Which of the the followi following ng is not a step step in in the graphica graphicall method method Draw the the constraint constraint bound boundary ary line for for each function functional al constrai constraint nt Find Find the the feasib feasible le region region Find Find the optim optimal al soluti solution on using using a straigh straight-ed t-edge ge Use Use Exc Excel el Solv Solver er
2
Given the following two constraints, which solution is a feasible solution for a maximization 6
problem? Constraint 1 : 4 X 1 + 3 X2 ≤ 18, Constraint Constraint 2: X 1 – X2 ≤ 3
a.
(X1, X2 ) = (1, 5).
b.
(X1, X2 ) = (4, 1).
c.
(X1, X2 ) = (4, 0).
d.
(X1, X2 ) = (2, 1).
7
Sensitiv Sensitivity ity analys analysis is is used used for for the the followin following g purpose purpose To check the effect on the recommendations of a model if the estimates turn out to be wrong
a. b. c. d. 8 a. b.
c. d. 9 a. b. c. d. 10 a. b. c. d. 11 a.
To check check ifif the solut solution ion is corr correct ect It is only used used for for the the graph graphical ical solution solution None of the above If the availability of an additional unit of a resource has any effect on the Objective Function, then that constraint is said to be A Bindi Binding ng Const Constrai raint nt A Non Non-Bi -Bind nding ing Constr Constrain aintt A Funct Function ional al Cons Constra traint int A Giv Given en Cons Constr trai aint nt Which of the following is not a component of a mathematical model for decision making? Deci Decisi sion on vari variab able les. s. A spre spread adsh shee eett Con Constrai train nts Para Param meter eterss A constra constraint int in in a mathe mathematic matical al model model is A variable variable represen representing ting the the decisi decision on to be be made made An inequalit inequality y or equation equation that restric restricts ts the values values of the decisio decision n variables. variables. A measu measure re of of the the perform performance ance of the the model model The The sal sales es fore foreca cast st.. Which of the following may not be in a linear programming formulation? <=
b. c. d.
12 a. b. c. d. 13 a. b. c. d. 14 a.
b. c. d. 15 a. b. c. d. 16 a. b. c. d. 17
> = a. and c. only A linear programming model is characterized by Continuous variables that can assume any value Integer variables only Binary integers only All of the above If the right-hand side value of a constraint in a two variable linear programming problems is changed, then The optim optimal al measur measure e of performan performance ce may may change change A parallel parallel shift shift must must be made made in the graph graph of that that constrain constraintt The optima optimall values values for one or more more of the decisio decision n variables variables may may change change All of the above Which if the following is true for Shadow Price 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
Shadow price is associated with the functional constraint (Left Hand Side of a Constraint) Shadow price is only linked to the decision variables All above statements are true In a Binary Integer Programming Problem, Binary variables can have the following values 0 1 Any integer value a. and b. only Which of the following is a probable reason for choosing simulation as a decision-making tool? The situation is too complex for a mathematical model Users are able to understand the model There is a limited time in which to obtain results a. and b. only Which of the following is considered to be a main advantage of simulation?
a. b. c. d. 18 a. b.
c. d. 19 a. b. c. d. 20 a. b. c. d. 21 a. b. c. d. 22 a. b. c. d. 23
It permits experimentation with the system. It generates an optimum solution. It compresses time a. and c. only 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 + B + C <= 2 A + B + C >= 2 A+B+C=2 None of the above The 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 Objective Function Constraint A Feasible Solution None of the above Which of the following is true at the break-even point? The fixed cost equals the variable cost The production quantity equals the sales forecast The company will neither make nor lose money on the product The profit equals the cost Enlightened Enlightened future managers do not need to know which which of the the following? following? When When managem management ent scienc science e can and and cannot cannot be appli applied. ed. How to apply apply the the major major techniq techniques ues of of manageme management nt science science.. How to inter interpret pret the the results results of a manag managemen ementt science science study. study. The mathemati mathematical cal theory theory behind behind the technique techniquess of management management science science Which of the following is not a category of linear programming problems? Resource-allocation problems Cost-benefit-tradeoff problems. Transportation problems All of the above are categories of linear programming problems Pure Transportation problems problems have the following type of constraints
a. b. c. d. 24 a. b. c. d. 25 a. b. c. d. 26 a. b. c. d. 27 a. b. c. d. 28 a. b. c. d. 29 a. b. c.
>= <= > None of the above Resource-allocation problems typically have which of the following type of constraints >= (Benefit Constraint) Constraint) <= (Resource Constraint) = (Fixed Requirement Constraint) All of the above Good Excel modeling practice includes the following Shading Shading cells to differentiate types of cells Use relative and absolute referencing to copy formulas Use Range Names All of the above Cost-benefit Cost-benefit tradeoff problems typically have which of the following type of constraints >= (Benefit Constraint) <= (Resource Constraint) = (Fixed Requirement Constraint) All of the above Mixed problems may have which of the following type of constraints >= (Benefit Constraint) Constraint) <= (Resource Constraint) = (Fixed Requirement Constraint) All of the above Which of the following is an assumption of assignment problems? The number of assignees and the number of tasks are the same The objective is to minimize the number of assignments not made Each task is to be performed by exactly one assignee a. and c. only A coefficient in the objective function is said to be sensitive if Even a small change in its value can change the optimal solution A large change in its value is needed to change the optimal solution Its shadow price is small
d. 30 a. b. c. d. 31 a.
b. and c. only What-if analysis: May be done graphically for problems with two decision variables May involve changes in the right-hand side values May increase a manager's confidence in the model that has been formulated All of the above Which of the following is not a benefit of what-if analysis It pinpoints the sensitive parameters of the model
b.
It gives the new optimal solution if conditions change after a study has been completed It tells management what policy decisions to make b. and c. only Which of the following statements is correct when making decisions? The sum of the state of nature probabilities must be 1 Every probability must be greater than or equal to 0 All probabilities are assumed to be equal a. and b. only. Following is not a feature of Bayes’ Decision Rule It accounts for all the states of nature and their probabilities The expected payoff can be interpreted as what the average payoff would become if the same situation were repeated many times Bayes’ decision rule directly uses the prior probabilities Always fixed and uniform values are assigned to the prior probabilities Which is considered to be a major advantage of using Bayes’ Decision Rule?
c. d. 32
a. b. c. d. 33 a. b. c. d. 34 a. b. c.
d.
There usually is considerable uncertainty involved in assigning values to the prior probabilities It accounts for all the states of nature and their probabilities Prior probabilities inherently are at least largely subjective in nature 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
The objective function of a linear programming programming model is given as: Maximize Z = x 1 + 2 x2 35
Subject to Constraint Constraint 1: x 1 + x2 ≤5, Constraint 2: x1 + 3 x2 ≤9 What is the objective objective function value if (x 1, x2) = (1,1) is used as a possible solution.
a. b. c. d.
36
3 5 7 None None of the the abo above ve Following is an infeasible solution for the linear programming model given below:: Maximize Z = x 1 + 2 x2
Subject to Constraint Constraint 1: x 1 + 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 None of the the abo above ve
37 a. b.
c. d. 38 a. b. c. d.
Which if the following statement is not true for a graphical solution to a linear programming model: In a minimization problem, the optimal solution improves if the objective function line is brought closer to the origin A graphical solution method can solve any linear programing problem without any restrictions on the number of decision variables involved In a maximization problem, the value of objective function improves as we move away from origin. None of the above The decision variables are constrained to take only positive values by the following Non Negativity Constraints Functional Constraints Right Hand Side of all constraints All of the above
39 a. b. c. d.
For a following minimization problem shown in a graph, the objective function is given by P = Y + 2X, What is the optimal solution (X,Y) = (0,9) (X,Y) = (8,3) (X,Y) = (4,3) (X,Y) = (15,5)
a. b. c. d.
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? (D,W) = (0,6) (D,W) = (2,6) (D,W) = (4,3) (D,W) = (4,0)
41 a. b. c. d.
When solving a maximization problem graphically, the goal is: To move the objective function line in, toward the origin, as far as possible The goal is to move the objective function line away from the origin The constraints are defined by greater than or equal to (≥) signs None of the above
40
42 a. b. c.
d. 43 a. b. c. d. 44 a. b. c. d. 45 a. b. c. d. 46 a. b. c. d. 47 a. b.
Following is true when solving a minimization problem graphically to find optimal solutions The goal is to move the objective function line in, toward the origin, as far as possible The goal is to move the objective function line away from the origin The constraints are defined by less than or equal to (≤) signs None of the above Which of the following is not a step taken in a typical management science study? Define the problem and gather data Formulate a model Apply the model and develop recommendations All of the above are typical steps in a management science study Which of the following is not a major step in the process of modeling with spreadsheets Plan Build Test All of the above. Which of the following are useful steps in the planning stage? Visualize where you want to finish Do some calculations by hand Sketch out a spreadsheet All of the above. A linear programming mathmatical model does not contain which of the following components Data. Decisions Constraints A spreadsheet The following statement is true: 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. 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. d. 48 a.
b. c. d. 49 a. b. c. d.
50
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 All of the above are true statements The Following statement is true A coefficient in the objective function is said to be sensitive if even a small change in its value can change the optimal solution 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 A coefficient in the objective function is said to be sensitive if its shadow price is small. All of the above statements are true 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? 50% 50% of the allowable increase of that coefficient 100% 50% of the range of optimality A linear programming model given below: Maximize Z = x 1 + 2 x2 Subject to Constraint Constraint 1: x 1 + x2 ≤5, Constraint 2: x1 + 3 x2 ≤9. What is the objective function value if (x 1, x2) = (3,1) is used as a possible solution?
a. b.
4 5
c. d.
7 None None of the the abo above ve
