Introduction to Management Sciencetestbank360.eu/sample/test-bank-introduction-to... · · 2017-03-03Test Item File Martha Wilson California State University, Sacramento Upper Saddle

Test Item File

Martha Wilson California State University , Sacramento

Upper Saddle River, New Jersey 07458

Introduction to Management Science

Bernard W. Taylor III

Full file at http://testbank360.eu/test-bank-introduction-to-management-science-with-student-cd-9th-edition-taylor

Contents Chapter 1 Management Science 1

Chapter 2 Linear Programming: Model Formulation and Graphical Solution 21

Chapter 3 Linear Programming: Computer Solution and Sensitivity Analysis 45

Chapter 4 Linear Programming: Modeling Examples 74

Chapter 5 Integer Programming 96

Chapter 6 Transportation, Transshipment, and Assignment Problems 120

Chapter 7 Network Flow Models 144

Chapter 8 Project Management 169

Chapter 9 Multicriteria Decision Making 195

Chapter 10 Nonlinear Programming 222

Chapter 11 Probability and Statistics 235

Chapter 12 Decision Analysis 265

Chapter 13 Queuing Analysis 297

Chapter 14 Simulation 320

Chapter 15 Forecasting 347

Chapter 16 Inventory Management 377

Module A The Simplex Solution Method 406

Module B Transportation and Assignment Solution Methods 426

Module C Integer Programming: The Branch and Bound Method 447

Module D Nonlinear Programming: Solution Techniques 462

Module E Game Theory 473

Module F Markov Analysis 488

Problem difficulty levels are represented as:

Diff 1 - Easy Diff 2 - Moderate Diff 3 - Difficult


Chapter 1Management Science

True/False

1) Management science involves the philosophy of approaching a problem in a subjectivemanner.

Answer: FALSEDiff: 1Key words: scientific approach

2) Management science encompasses a logical approach to problem solving.

Answer: TRUEDiff: 1Key words: scientific approach, problem solving

3) Once management scientist makes his or her decision and recommendation to management,then typically, his or her involvement with the problem is finished.

Answer: FALSEDiff: 2Key words: management science, management scientist

4) A variable is a symbol used to represent an item that can take on any value.

Answer: TRUEDiff: 1Key words: variable

5) Parameters are unknown, constant values that are not coefficients of variables in equations.

Answer: FALSEDiff: 1Key words: parameter

6) Data are pieces of information from the problem environment.

Answer: TRUEDiff: 1Key words: data

7) A model is a functional relationship including variables, parameters, and equations.

Answer: TRUEDiff: 1Key words: model, management science techniques

1


Management Science - Chapter 1

8) A management science technique usually applies to a specific model type.

Answer: TRUEDiff: 1Key words: models, management science techniques

9) A management science solution can be either a recommended decision or information thathelps a manager make a decision.

Answer: TRUEDiff: 1Key words: solution, management science solution

10) Management science modeling techniques provide results that are known with certainty.

Answer: FALSEDiff: 2Key words: management science modeling techniques, certainty

11) A constraint represents the limitation of management science techniques.

Answer: FALSEDiff: 2Key words: constraints, management science techniques

12) The term decision analysis refers to testing how a problem solution reacts to changes in one ormore of the model parameters.

Answer: FALSEDiff: 1Key words: sensitivity analysis, parameter changes

13) Fixed costs depend on the number of items produced.

Answer: FALSEDiff: 1Key words: fixed cost, break-even analysis

14) Variable costs are independent of volume and remain constant.

Answer: FALSEDiff: 1Key words: variable cost, break-even analysis

15) Total cost equals the fixed cost plus the variable cost per unit divided by volume.

Answer: FALSEDiff: 1Key words: total cost, break-even analysis

2



16) Profit is the difference between total revenue and total cost.

Answer: TRUEDiff: 1Key words: profit, break-even analysis

17) The break-even point is the volume that equates total revenue with total cost and profit iszero.

Answer: TRUEDiff: 1Key words: break-even analysis

18) In general, an increase in price increases the break even point if all costs are held constant.

Answer: FALSEDiff: 1Key words: break-even analysis

19) If variable costs increase, but price and fixed costs are held constant, the break even point willdecrease.

Answer: FALSEDiff: 2Key words: break-even analysis

20) Managers utilize spreadsheets to conduct their own analyses in management science studies.

Answer: TRUEDiff: 2Key words: spreadsheets

21) Management science techniques focus primarily on 3 specific steps of the management scienceprocess (observation, model construction and implementation) to find an appropriate solutionto a problem.

Answer: FALSEDiff: 2Key words: mgt sci modeling techniques, steps of the scientific method

22) Management science modeling techniques focus on model construction and problem solution.

Answer: TRUEDiff: 2Key words: mgt science model techniques, model constr, prob solution

3



23) Enterprise Resource Planning (ERP) system is a data oriented decision support system thatutilizes specific management science solution procedures to solve individual problems such ascost-volume analysis.

Answer: FALSEDiff: 1Key words: decision support systems

Fill in the Blank

24) A __________ is a symbol used to represent an item that can take on any value.

Answer: variableDiff: 1Key words: variable, management science process

25) __________ are unknown, constant values that are not coefficients of variables in equations.

Answer: ParametersDiff: 1Key words: model, parameters

26) __________ are pieces of information from the problem environment.

Answer: DataDiff: 1Key words: data

27) A __________ is a functional relationship including variables, parameters, and equations.

Answer: modelDiff: 1Key words: model

28) __________ techniques consist of models that are represented as diagrams, presenting apictorial representation of the system being analyzed.

Answer: NetworkDiff: 1Key words: management science, networks

29) __________ techniques provide results that contain uncertainty, unlike mathematicalprogramming techniques which are deterministic.

Answer: ProbabilisticDiff: 1Key words: management science techniques, probabilistic techniques

4



30) __________ are independent of volume of goods produced and remain constant.

Answer: Fixed costsDiff: 1Key words: fixed cost, break-even analysis

31) __________ depend on the number of items produced.

Answer: Variable costsDiff: 1Key words: variable cost, break-even analysis

32) __________ is the difference between total revenue and total cost.

Answer: ProfitDiff: 1Key words: profit, break-even analysis

33) The __________ is the volume that equates total revenue with total cost and profit is zero.

Answer: break-even pointDiff: 1Key words: break-even analysis

34) A __________ represents a limitation to achieving maximum profits due to limited resources.

Answer: constraintDiff: 1Key words: constraint, model development

35) The __________ can be noted as Z, and represents the goal of the firm.

Answer: objective functionDiff: 1Key words: objective function, model development

36) A __________ is a computer-based system that helps decision-makers address complexproblems that involve different parts of an organization and operations.

Answer: decision support systemDiff: 1Key words: decision support systems

Problem Solving

37) The relationship d = 5000 - 25p describes what happens to demand (d) as price (p) varies.Price can vary between $10 and $50. How many units can be sold when the price is $10?

Answer: 4750Diff: 1Key words: break-even analysis

5



38) There is a fixed cost of $50,000 to start a production process. Once the process has begun, thevariable cost per unit is $25. The revenue per unit is projected to be $45. Write a mathematicalexpression for total cost.

Answer: C(x) = 50000 + 25xDiff: 1Key words: break-even analysis

39) There is a fixed cost of $50,000 to start a production process. Once the process has begun, thevariable cost per unit is $25. The revenue per unit is projected to be $45. Write an expressionfor total revenue.

Answer: R(x) = 45xDiff: 1Key words: break-even analysis

40) There is a fixed cost of $50,000 to start a production process. Once the process has begun, thevariable cost per unit is $25. The revenue per unit is projected to be $45. Write an expressionfor total profit.

Answer: P(x) = 45x - (50000 + 25x)Diff: 1Key words: break-even analysis

41) There is a fixed cost of $50,000 to start a production process. Once the process has begun, thevariable cost per unit is $25. The revenue per unit is projected to be $45. Find the break-evenpoint.

Answer: X = 2500Diff: 2Key words: break-even analysis

42) Administrators at a university will charge students $150 to attend a seminar. It costs $3000 toreserve a room, hire an instructor, and bring in the equipment. Assume it costs $25 per studentfor the administrators to provide the course materials. How many students would have toregister for the seminar for the university to break even?

Answer: 24Diff: 2Key words: break-even analysis

43) Administrators at a university are planning to offer a summer seminar. It costs $3000 toreserve a room, hire an instructor, and bring in the equipment. Assume it costs $25 per studentfor the administrators to provide the course materials. If we know that 20 people will attend,what price should be charged per person to break even?

Answer: $175Diff: 2Key words: break-even analysis

6



44) A newly opened bed-and-breakfast projects the following:Monthly fixed costs $6000Variable cost per occupied room per night $20Revenue per occupied room per night $75Write the expression for total cost per month (30 days).

Answer: C(x) = 6000 + 20(30)xDiff: 2Key words: break-even analysis

45) A newly opened bed-and-breakfast projects the following:Monthly fixed costs $6000Variable cost per occupied room per night $20Revenue per occupied room per night $75Write the expression for total revenue per month (30 days).

Answer: R(x) = 75(30)xDiff: 2Key words: break-even analysis

46) A newly opened bed-and-breakfast projects the following:Monthly fixed costs $6000Variable cost per occupied room per night $20Revenue per occupied room per night $75If there are 12 rooms available, what percentage of rooms would have to be occupied, onaverage, to break even?

Answer: 3.64 = 4 rooms - 4/12 = 33%Diff: 3Key words: break-even analysis

47) A script writer has received an advance against royalties of $10000. The royalty rate is $1 forevery performance in the US, and $1.35 for every performance outside the US. Define variablesfor this problem.

Answer: X1 = # of performances in the U.S.X2 = # of performances outside the U.S.

Diff: 3Key words: break-even analysis

48) A script writer has received an advance against royalties of $10,000. The royalty rate is $1 forevery performance in the US, and $1.35 for every performance outside the US. Write anexpression that could be used to compute the number of performances in order to cover theadvance.

Answer: 10000 = 1x1 + 1.35x2Diff: 3Key words: break-even analysis

7



49) Students are organizing a ʺBattle of the Bandsʺ contest. They know that at least 100 peoplewill attend. The rental fee for the hall is $150 and the winning band will receive $500. In orderto guarantee that they break even, how much should they charge for each ticket?

Answer: $6.50Diff: 2Key words: break-even analysis

50) A manufacturer buys peas for vegetable pies from 2 cooperatives. The price per unit is $6 fromcooperative A, and $5.50 per unit from cooperative B. Define variables that would tell howmany units to purchase from each source.

Answer: X1 = # of units from cooperative AX2 = # of units from cooperative B

Diff: 3Key words: break-even analysis, variable definition

51) A manufacturer buys peas for vegetable pies from 2 cooperatives. The price per unit is $6 fromcooperative A, and $5.50 per unit from cooperative B. Develop an objective function thatwould minimize the total cost.

Answer: Min 6x1 + 5.5x2Diff: 3Key words: objective function, break-even analysis, model development

52) A manufacturer buys peas for vegetable pies from 2 cooperatives. The price per unit is $6 fromcooperative A, and $5.50 per unit from cooperative B. The manufacturer needs at least 12000units of peas. Cooperative A can supply up to 8000 units, and cooperative B can supply at least6000 units. Develop constraints for these conditions.

Answer: XA + XB ≤ 12000XA ≤ 8000XB ≥ 6000

Diff: 3Key words: constraints, model development

53) A manager of the cereal bar at the college campus has determined that the profit made foreach bowl of Morning Buzz cereal sold, x, is equal to: Z = $4x - 0.5x. Each bowl of MorningBuzz weighs 6 ounces, and the manager has 12 lbs (192 ounces) of cereal available each day,which can be written as the constraint, 6x ≤192. How much profit will be made from MorningBuzz if it is all sold in one day?

Answer: $112Diff: 2Key words: model development

8



54) The College Coffee Cafe buys tea from 3 suppliers. The price per pound is $15.00 fromsupplier A, $17.50 from supplier B, and $21.00 from supplier C. They have budged $175 topurchase the tea. The cafe needs at least 12 pounds of tea, and supplier C can supply no morethan 4 pounds. Develop constraints for these conditions.

Answer: 15.00XA + 17.50 XB + 21XC ≤175XA +XB +XC ≥ 12XC ≤ 4

Diff: 3Key words: constraints, model development

55) The College Coffee Cafe receives a profit of $1.25 for each cup of house tea that they sell, $1.40for each cup of the premium brand, and $1.50 for each cup of their special blend that they sell.Develop an objective that maximizes profit.

Answer: Max 1.25x1 + 1.40x2 + 1.50 x3Diff: 2Key words: objective function, model development

Multiple Choice

56) The steps of the scientific method are:

A) problem definition, model construction, observation, model solution, implementation.

B) observation, problem definition, model construction, model solution, implementation.

C) model construction, problem definition, observation, model solution, implementation.

D) observation, implementation, problem definition, model construction, model solution.

Answer: BDiff: 1Key words: steps of sci method, prob solving approach, mgt sci process

57) A model is a functional relationship and include:

A) variables

B) parameters

C) equations

D) all of the above

Answer: DDiff: 1Key words: model

9



58) Which of the following is an equation or an inequality that expresses a resource restriction in amathematical model?

A) a decision variable.

B) data

C) an objective function.

D) a constraint.

E) a parameter.

Answer: DDiff: 2Key words: model, constraint

59) Which of the following is incorrect with respect to the use of models in decision making?

A) they improve understanding of the problem

B) they promote subjectivity in decision making

C) they are generally easy to use

D) they provide a systematic approach to problem solving

Answer: BDiff: 3Key words: model, problem solving

60) The field of management science

A) approaches decision making rationally with techniques based on the scientific method

B) is another name for decision science and for operations research

C) concentrates on the use of quantitative methods to assist managers in decision making

D) all of the above

Answer: DDiff: 1Key words: management science, operations research

61) The processes of problem observation

A) cannot be done until alternatives are proposed

B) requires consideration of multiple criteria

C) is the first step of decision making

D) is the final step of problem solving

Answer: CDiff: 1Key words: observation, problem observation, management science process

10



62) The limits of the problem and the degree to which it pervades other units other units in theorganization must be included during the __________ step of the management science process.

A) observation

B) definition

C) solution

D) implementation

Answer: BDiff: 1Key words: management science process

63) __________ involves determining the functional relationship between variables, parametersand equations

A) Problem observation

B) Problem definition

C) Model construction

D) Model solution

E) Model implementation

Answer: CDiff: 1Key words: management science process, model construction

64) Management science __________ can either be a recommended decision or information thathelps a manager make a decision.

A) model implementation

B) model construction

C) problem definition

D) model solution

E) problem formulation

Answer: DDiff: 2Key words: management science process, model solution

65) The quantitative analysis approach requires

A) mathematical expressions for the relationship

B) uncomplicated problems

C) the manager to have prior experience with similar problems

D) all of the above

Answer: ADiff: 2Key words: management science, operations research, quantitative analysis

11



66) The result of an effective decision making process should be monitored in order to

A) reveal wrong assumptions

B) reveal errors in the implementation

C) insure the achievement of desired results

D) all of the above

Answer: DDiff: 2Key words: decision making process

67) Which of the following is not a general approach to decision-making?

A) establishing priorities

B) analysis of tradeoffs

C) an emphasis on subjectivity

D) a systemʹs approach

Answer: CDiff: 2Key words: decision making, management science

68) The management science process does not include

A) problem definition

B) feedback

C) implementation

D) subjective preference

E) information

Answer: DDiff: 2Key words: management science process

69) The indicator that results in total revenues being equal to total cost is called the

A) marginal cost

B) marginal volume

C) break-even point

D) profit mix

Answer: CDiff: 1Key words: break-even analysis

12



70) Variable cost

A) depends on the number of units produced

B) plus marginal cost equals fixed cost

C) is equal to total cost in deterministic models

D) all of the above

Answer: ADiff: 2Key words: break-even analysis

71) The components of break-even analysis are

A) volume, cost and profit

B) volume and cost

C) cost and profit

D) volume and profit


72) __________ are generally independent of the volume of units produced and sold.

A) Fixed costs

B) Variable costs

C) Profits

D) all of the above


73) The purpose of break-even analysis is to determine the number of units of a product to sellthat will

A) equal total revenue with total cost

B) be larger than total revenue compared to total cost

C) be smaller than total revenue compared to total cost

D) none of the above


13



74) Variable cost includes

A) raw materials and resources

B) direct labor and packaging

C) material handling and freight

D) all of the above

Answer: DDiff: 2Key words: break-even analysis

75) Which variable is not a component of break-even analysis?

A) fixed costs

B) variable costs

C) number of employees

D) total costs

E) number of customers


76) At the break-even point

A) Total revenue equals total cost

B) profit is zero

C) revenue is maximized

D) A and B


77) An increase in price with everything else remaining constant

A) decreases the break-even point

B) raises the break-even point

C) keeps the break-even point at the same level

D) does not affect the level of the break-even point


14



78) A decrease in price with everything else remaining constant


B) raises the break-even point



Answer: BDiff: 2Key words: break-even analysis

79) The term __________ refers to testing how a problem solution reacts to changes in one or moreof the model parameters.

A) graphical solution

B) decision analysis

C) decision science

D) sensitivity analysis

E) break-even analysis

Answer: DDiff: 2Key words: sensitivity analysis, modeling process

80) A decrease in fixed costs with everything else remaining constant


B) increases the break-even point




81) An increase in fixed costs with everything else remaining constant


B) increases the break-even point




15



82) EKA manufacturing company produces Part # 2206 for the aerospace industry. Each unit ofpart # 2206 is sold for $15. The unit production cost of part # 2206 is $3. The fixed monthly costof operating the production facility is $3000. How many units of part # 2206 have to be sold ina month to break-even?

A) 166.67

B) 200

C) 250

D) 500

E) 1000


83) EKA manufacturing company produces Part # 2206 for the aerospace industry. The unitproduction cost of part # 2206 is $3. The fixed monthly cost of operating the production facilityis $3000. Next monthʹs demand for part # 2206 is 200 units. How much should the companycharge for each unit of part # 2206 to break-even?

A) 10

B) 12

C) 15

D) 18

E) 20


84) Administrators at a university will charge students $150 to attend a seminar. It costs $3000 toreserve a room, hire an instructor, and bring in the equipment. Assume it costs $25 per studentfor the administrators to provide the course materials. How many students would have toregister for the seminar for the university to break even?

A) 16

B) 18

C) 20

D) 24

E) 30


16



85) A university is planning a seminar. It costs $3000 to reserve a room, hire an instructor, andbring in the equipment. Assume it costs $25 per student for the administrators to provide thecourse materials. If we know that 20 people will attend, what price should be charged perperson to break even?

A) 100

B) 120

C) 150

D) 175

E) 200


86) Which of the following statements is false?

A) Decision models selectively describe the managerial situation.

B) Decision models consider all factors from the real world.

C) Decision models designate performance measures that reflect objectives.

D) Decision models designate decision variables.

Answer: BDiff: 2Key words: models, decision models, modeling techniques

87) A difficult aspect of using spreadsheets to solve management science problems is:

A) obtaining the solution to standard management science problems

B) data entry

C) performing sensitivity analysis

D) setting up a spreadsheet with complex models and formulas

Answer: DDiff: 2Key words: computer solution, spreadsheets

88) Which of the following statements is false?

A) Common sense is one test of the validity of a model.

B) One way to validate a model is to predict history.

C) Models are usually built sequentially rather than iteratively.

D) Model validation means making sure that the available information obtained from theanalysis is understood in the context of the original real world situation.

Answer: CDiff: 3Key words: modeling, models, modeling techniques

17



89) Classification of management science techniques recognizes

A) linear mathematical programming techniques

B) probabilistic techniques

C) network and forecasting techniques

D) all of the above

Answer: DDiff: 1Key words: management science techniques, classification of techniques

90) Management science modeling techniques focus on

A) problem definition, model construction, problem solution and model implementation

B) problem definition, model construction and problem solution

C) model construction and problem solution

D) none of the above

Answer: CDiff: 2Key words: management science techniques, management science process

91) Linear mathematical programming techniques assume that all parameters in the models are

A) known with certainty

B) unknown

C) predictable

D) unpredictable

Answer: ADiff: 2Key words: management science techniques

92) Decision analysis is a __________ technique.

A) linear mathematical programming

B) probabilistic

C) network

D) simulation

E) non-linear programming technique

Answer: BDiff: 1Key words: management science techniques

18



93) Which one of the following techniques is not a mathematical programming technique?

A) linear programming models

B) transportation models

C) analytical hierarchy process

D) goal programming

E) integer linear programming technique

Answer: CDiff: 2Key words: management science techniques

94) Which one of the following management science methods is not a probabilistic technique?

A) linear programming models

B) decision analysis

C) queuing analysis

D) statistical analysis

E) none of the above

Answer: ADiff: 2Key words: management science techniques

95) A baker uses organic flour from a local farmer in all of his baked goods. For each batch ofbread (x1), he uses 4 lbs. For a batch of cookies (x2), he uses 3 pounds, and for a batch ofmuffins (x3) he uses 2 pounds. The local farmer can supply him with no more than 24 poundsper week. The constraint that represents this condition is:

A) x1 ≤ 8, x2 ≤ 8, x3 ≤ 8

B) x1+ x2 + x3 ≥ 24

C) x1 ≤ 6, x2 ≤ 8, x3 ≤ 12

D) x1+ x2 + x3 ≤ 24

E) 4x1+ 3x2 + 2x3 ≤ 24

Answer: EDiff: 3Key words: constraints

19



96) An objective function

A) is a part of a model

B) represents the objective of the firm

C) can represent costs or profits

D) A and B only

E) all of the above

Answer: EDiff: 2Key words: objective function, model construction

97) Larryʹs Fish Market buys salmon (S) for $5 per pound and a local whitefish (W) for $3.50 perpound. Larry wants to minimize his cost, but he cannot spend more than $160. The objectivefunction that minimizes these costs for Larry is:

A) 5S + 3.5W = 160

B) 5S + 3.5W ≤ 160

C) Min 5S + 3.5 W

D) Max 5S + 3.5 W

E) 5S + 3.5W ≥ 160

Answer: CDiff: 3Key words: objective function, model construction

20


Chapter 2Linear Programming:

Model Formulation and Graphical Solution

True/False

1) Linear programming is a model consisting of linear relationships representing a firmʹsdecisions given an objective and resource constraints.

Answer: TRUEDiff: 2Key words: model formulation

2) The objective function is a linear relationship reflecting the objective of an operation.


3) A constraint is a linear relationship representing a restriction on decision making.


4) A linear programming model consists of decision variables, constraints, but no objectivefunction.

Answer: FALSEDiff: 1Key words: model formulation

5) A feasible solution violates at least one of the constraints.

Answer: FALSEDiff: 2Key words: model formulation

6) Proportionality means the slope of a constraint or objective function line is not constant.

Answer: FALSEDiff: 2Key words: properties of linear programming models, proportionality

7) The terms in the objective function or constraints are not additive.

Answer: FALSEDiff: 2Key words: properties of linear programming models, additive

21


Linear Programming: Model Formulation and Graphical Solution - Chapter 2

8) The values of decision variables are continuous or divisible.

Answer: TRUEDiff: 2Key words: properties of linear programming models, divisible

9) All model parameters are assumed to be known with certainty.

Answer: TRUEDiff: 2Key words: properties of linear programming models

10) Linear programming models have an objective function to be maximized but not minimized.

Answer: FALSEDiff: 1Key words: properties of linear programming models, objective function

11) All linear programming models exhibit a set of constraints.

Answer: TRUEDiff: 1Key words: properties of linear programming models, constraints

12) Linear programming models exhibit linearity among all constraint relationships and theobjective function.

Answer: TRUEDiff: 1Key words: properties of linear prog models, linearity, proportionality

13) The equation 8xy = 32 satisfies the proportionality property of linear programming.

Answer: FALSEDiff: 2Key words: graphical solution, proportionality

14) Objective functions in linear programs always maximize profits.

Answer: FALSEDiff: 2Key words: properties of linear programming models, objective function

15) The feasible solution area represents contains infinite solutions to the linear program.

Answer: TRUEDiff: 1Key words: properties of linear programming models, feasible solution area

22



16) There is exactly one optimal solution point to a linear program.

Answer: FALSEDiff: 2Key words: properties of linear programming models, optimal solution pt

17) The following equation represents a resource constraint for a maximization problem:X + Y ≥ 20

Answer: FALSEDiff: 2Key words: properties of linear programming models, constraint

18) A minimization model of a linear program contains only surplus variables.

Answer: FALSEDiff: 1Key words: properties of linear programming models, surplus variables

19) In the graphical approach, once the feasible solution area and the optimal solution point havebeen determined from the graph, simultaneous equations are solved to determine the valuesof x1 and x2 at the solution point.

Answer: TRUEDiff: 2Key words: graphical solution

20) Slack variables are only associated with maximization problems.

Answer: FALSEDiff: 2Key words: graphical solution, slack variable

21) Surplus variables are only associated with minimization problems.

Answer: FALSEDiff: 2Key words: graphical solution, surplus variable

22) The graphical approach to the solution of linear programming problems can solve linearprogramming problems with more than two decision variables.

Answer: FALSEDiff: 1Key words: graphical solution

23) Graphical solution to linear programming problems has an infinite number of possibleobjective function lines.

Answer: TRUEDiff: 2Key words: graphical solution, objective function line

23



Fill in the Blank

24) __________ are mathematical symbols representing levels of activity.

Answer: Decision variablesDiff: 1Key words: decision variables, model formulation

25) The __________ is a linear relationship reflecting the objective of an operation.

Answer: objective functionDiff: 1Key words: objective function, model formulation

26) A __________ is a linear relationship representing a restriction on decision making.

Answer: constraintDiff: 1Key words: constraint, model formulation

27) An __________ solution violates at least one of the model constraints.

Answer: infeasibleDiff: 1Key words: constraint, infeasible solution

28) A graphical solution is limited to solving linear programming problems with only __________decision variables

Answer: twoDiff: 1Key words: graphical solution

29) The __________ solution area is an area bounded by the constraint equations.

Answer: feasibleDiff: 1Key words: graphical solution

30) Multiple optimal solutions can occur when the objective function line is __________ to aconstraint line.

Answer: parallelDiff: 2Key words: graphical solution, multiple optimal solutions

31) For a maximization problem if the problem is __________, the objective function can increaseindefinitely without reaching a maximum value.

Answer: unboundedDiff: 2Key words: graphical solution, unbounded problem

24



32) A linear programming problem the results in a solution that is __________ usually indicatesthat the linear program has been incorrectly formulated.

Answer: infeasibleDiff: 2Key words: graphical solution, infeasible solution

33) A __________ variable represents excess above a constraint requirement.

Answer: surplusDiff: 1Key words: graphical solution, surplus variable

34) If the objective function is parallel to a constraint, the linear program could have __________.

Answer: multiple optimal solutionsDiff: 2Key words: graphical solutions, multiple optimal solutions

35) The __________ property of linear programming models indicates that the values of all themodel parameters are known and are assumed to be constant.

Answer: certaintyDiff: 2Key words: properties of linear programming models, certainty

36) The __________ property of linear programming models indicates that the rate of change orslope of the objective function or a constraint is constant.

Answer: proportionality or linearityDiff: 2Key words: properties of linear programming models, certainty

37) The __________ property of linear programming models indicates that the decision variablescannot be restricted to integer values and can take on any fractional value.

Answer: divisibilityDiff: 2Key words: properties of linear programming models, divisibility

38) The constraint, 2X +XY violates the __________ property of linear programming.

Answer: proportionality or linearDiff: 1Key words: properties of linear programming models

25



Problem Solving

39) Consider the following minimization problem:Min z = x1 + 2x2s.t. x1 + x2 ≥ 300

2x1 + x2 ≥ 4002x1 + 5x2 ≤ 750x1, x2 ≥ 0

Which of the three constraints are binding?

Answer: constraint 1Diff: 3Key words: Graphical solution, simultaneous solution


2x1 + x2 ≥ 4002x1 + 5x2 ≤ 750x1, x2 ≥ 0

Which constraints are binding at the optimal solution? (x1 =250, x2 = 50)

Answer: constraints 1 and 3Diff: 1Key words: Graphical solution, simultaneous solution

41) Consider the following minimization problem:Min z = 1.5x1 + 2x2s.t. x1 + x2 ≥ 300

2x1 + x2 ≥ 4002x1 + 5x2 ≤ 750x1, x2 ≥ 0

What are the optimal values of x1, x2, and z?

Answer: x1 = 250, x2 = 50, z = 475Diff: 3Key words: graphical solution, simultaneous solution

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2x1 + x2 ≥ 4002x1 + 5x2 ≤ 750x1, x2 ≥ 0

If the objective function becomes Min 7x1 + 6x2, what constraints will be binding?

Answer: constraints 1 and 2Diff: 3Key words: graphical solution, sensitivity analysis

43) Consider the following linear program:

MAX Z = 60A + 50Bs.t. 10A + 20B ≤ 200

8A + 5B ≤ 80A ≥ 2B ≥ 5

Solve this linear program graphically and determine the optimal quantities of A, B, and thevalue of Z.

Answer: Solution shown below.

Diff: 2Key words: graphical linear programming

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44) A graphical representation of a linear program is shown below. The shaded area representsthe feasible region, and the dashed line in the middle is the slope of the objective function.

If this is a maximization, which extreme point is the optimal solution?

Answer: EDiff: 1Key words: graphical solution, extreme points, feasible region

45) A graphical representation of a linear program is shown below. The shaded area representsthe feasible region, and the dashed line in the middle is the slope of the objective function.

If this is a minimization, which extreme point is the optimal solution?

Answer: ADiff: 2Key words: graphical solution, extreme points, feasible region

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