MULTIPLE CHOICE. Choose the letter corresponding to the one alternative that best completes the statement or answers the question. 1. Which of the following are assumptions or requirements of the transportation problem? a. goods are the same, regardless of source b. there must be multiple sources c. shipping costs per unit do not vary with the quantity shipped d. all of the above 2. In a trans-shipment problem, items may be transported a. from source to source b. from one destination to another c. from sources to trans-shipment point d. from trans-shipment points to destinations e. all of the above 3. An assignment problem is a special form of transportation problem where all supply and demand values equal a. 0 b. 1 c. 2 d. greater than 1 e. none of the above 4. The trans-shipment model is an extension of the transportation model in which intermediate transshipment points are between the sources and destinations. a. decreased b. deleted c. subtracted d. added 5. In the process of evaluating location alternatives, the transportation model method minimizes the a. total demand b. total supply c. total shipping cost d. number of destinations 6. Arcs in a trans-shipment problem a. indicate the direction of the flow b. must connect every node to a trans-shipment node c. represent the cost of shipments d. all of the above 7. A trans-shipment constraint must contain a variable for every entering or leaving the node. a. leave b. axe c.arc d. flow Page 1 of 19
8. Transportation, assignment, and trans-shipment problems have wide applications and belong to a class of linear programming problems called a. distance problems. b. network flow problems. c. distribution design problems. d. minimum cost problems. 9. The problem which deals with the distribution of goods from several sources to several destinations is the a. network problem b. transportation problem c. assignment problem d. trans-shipment problem 10. The parts of a network that represent the origins are a. the axes b. the flow c. the nodes d. the arrows 11. A linear program where the slope of the objective function is the same as the slope of one of the constraints results in a. alternative optimal solutions b. unique optimal solution c. infeasibility d. unbounded feasible region 12. In the linear programming formulation of a transportation network a. there is one constraint for each node. b. there is one variable for each arc. c. the sum of variables corresponding to arcs out of an origin node is constrained by the supply at that node. d. All of the alternatives are correct. 13. Constraints in a trans-shipment problem a. correspond to arcs. b. include a variable for every arc. c. require the sum of the shipments out of an origin node to equal supply. d. All of the alternatives are correct. 14. In a trans-shipment problem, shipments a. cannot occur between two origin nodes. b. cannot occur between an origin node and a destination node. c. cannot occur between a trans-shipment node and a destination node. d. can occur between any two nodes. 15. The constraint x 14 + x 24 x 47 x 48 = 0, can only be a constraint a. origin b. trans-shipment c. destination d. all of the above. Page 2 of 19
16. An unbalanced transportation problem with demand exceeding supply a. requires a dummy demand b. requires a dummy supply c. both a. and b. d.neither a. nor b. 17. When a route in a transportation problem is unacceptable, a. the corresponding variable must be removed from the LP formulation. b. the corresponding variable must be constrained to zero. c. either a. or b d. neither a. nor b Questions #18 through #22. A linear trend analysis was performed on monthly sales (in $000) of a computer store over the 60 months (x = 1, 2,..., 60) from January 2004 through December 2008. Below is partial output from the associated linear regression analysis using a certain statistical package: Regression Analysis - Linear model: Y = a + b*x Dependent variable: sales_000 Independent variable: month Stand T Parameter Estimate Error Statistic P-Value Intercept 93.6257 2.55166 36.6921 0.0000 Slope 0.646287 0.0727694 0.0000 Analysis of Variance Source Sum of Squares Df Mean Square F-Ratio P-Value ---------------------------------------------------------------------------------------------------------------------------------- Model? 1 7526.28 78.88 0.0000 Residual? 58 95.4175 Total (Corr.) 13060.5 59 R-squared = 57.6263 percent Standard Error of Est. = 9.76819 18. The sample coefficient of correlation is approximately: A. 7.591 B. 0.7591 C. 57.6263 D. 0.576263 E. not possible to determine from available information 19. The sum of squares for error is approximately: A. 9.76819 B. 13,060.5 C. 7,526.28 D. 5,534.21 Page 3 of 19
20. The value of the test statistic for testing the significance of β 1, is approximately: A. 8.8813 B. 36.6921 C. 78.88 D. 0 E. none of the above 21. Using the sample regression equation to forecast monthly sales in 2009, the forecast for January 2009 would be approximately: A. $94,272 B. $132,403 C. $133,049 D. $93,665 E. none of the above 22. The value of the test statistic for testing the significance of ρ would be: A. approximately 0.759 B. approximately 0.576 C. approximately zero D. equal to the value of the test statistic for testing the slope E. not possible to determine from available information Questions #23 through #27. The manager of North York Furniture Co. has been reviewing weekly advertising expenditures. During the past six months, all advertisements for the store have appeared in the local newspaper, Toronto Star. The number of ads per week has varied from one to seven. The sales staff has been tracking the number of customers who enter the store each week. A simple linear regression model using the least squares method is being considered to estimate the number of customers who enter the store within a week, given the number of advertisements appearing in the local newspaper during the week. Below is partial linear regression analysis output from a certain statistical package. Regression Analysis - Linear model: Y = a + b*x Dependent variable: no_of_customers Independent variable: no_of_ads Standard T Parameter Estimate Error Statisti P-Value Intercept 296.92 64.3052 4.61735 0.0001 Slope 21.356 14.2833 1.49517 0.1479 Analysis of Variance Source Sum of Squares Df Mean Square F-Ratio P-Value Model? 1? 2.24 0.1479 Residual? 24? Total (Corr.) 463802.0 25 Correlation Coefficient =? R-squared = 8.52106 percent Standard Error of Est. = 132.96 Page 4 of 19
23. If the least squares line were to be used, a point estimator for the expected number of customers in a week when no advertisement is placed in the local newspaper is approximately A. 318 B. 0 C. 297 D. 21 24. If the least squares line were to be used, a point estimator for the expected number of customers in a week when 5 advertisements are placed in the local newspaper is approximately A. 21 B. 404 C. 107 D. 297 25. The sum of squares for error is approximately A. 39520.8 B. 424281.2 C. 463802.0 D. not possible to determine from the available information 26. The proportion of the variation in no_of_customers that is explained by the variation in no_of ads is approximately A. 0.085 B. 0.915 C. 0.007 D. 0.292 E. not possible to determine from the available information 27. A test of hypothesis concerning the coefficient of correlation ρ with H A : ρ 0 at the 10% level of significance A. is a one-tailed test B. yields a test statistic value of 4.61735 C. would lead to a decision to reject the null hypothesis D. would have as decision rule to reject H o if t> 1.711 E. none of the above is true 28. Types of integer programming models are. a. total/all b. 0-1 c. mixed d. all of the above 29. In a integer model, some solution values for decision variables are integer and others can be non-integer. a. total b. 0-1 c. mixed d. all of the above Page 5 of 19
30. Which of the following is not an integer linear programming problem? a. pure integer b. mixed integer c. 0-1 integer d. continuous 31. In using rounding of a linear programming model to obtain an integer solution, the solution is a. always optimal and feasible b. sometimes optimal and feasible c. always optimal d. always feasible e. never optimal and feasible 32. If x 1 + x 2 is less than or equal to 500y 1 and y 1 is 0-1, then x 1 and x 2 will be if y 1 is 0. a. equal to 0 b. less than 0 c. more than 0 d. equal to 500 e. one of the above 33. If a maximization linear programming problem consist 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. a. always, optimal b. always, non-optimal c. never, non-optimal d. sometimes, optimal e. never, optimal 34. If we are solving a 0-1 integer programming problem, the constraint x 1 + x 2 1 is a constraint. a. multiple choice b. mutually exclusive c. conditional d. co-requisite e. none of the above 35. If we are solving a 0-1 integer programming problem, the constraint x 1 + x 2 = 1 is a constraint. a. multiple choice mutually exclusive c. conditional d. corequisite e. none of the above 36. If we are solving a 0-1 integer programming problem, the constraint x 1 x 2 is a constraint. a. multiple choice b. mutually exclusive c., conditional d. co-requisite e. none of the above Page 6 of 19
37. If we are solving a 0-1 integer programming problem, the constraint x1 = x2 is a constraint. a. multiple choice b. mutually exclusive c. conditional d. corequisite e. none of the above 38. For a maximization integer linear programming problem, feasible solution is ensured by rounding non-integer solution values if all of the constraints are less-than -or equal- to type. a. up and down b. up c. down d. up or down 39. The linear programming relaxation contains the and the original constraints of the integer programming problem, but drops all integer restrictions. a. different variables b. slack values c. objective function d. decision variables e. surplus variables 40. If the optimal solution to the linear programming relaxation problem is integer, it is to the integer linear programming problem. a. real solution b. a degenerate solution c. an infeasible solution d. the optimal solution e. a feasible solution 41. Binary variables are a. 0 or 1 only b. any integer value c. any continuous value d. any negative integer value 42. Max Z=5x 1 +6x 2 Subject to: 17x 1 + 8x 2 136 3x 1 +4x 2 36 x 1, x 2 0 and integer What is the optimal solution? a.x1=6, x2=4, Z=54 b. x1= 3, x2 6, Z=51 c. x1=2, x2=6, Z=46 d. x1= 4, x2= 6, Z=56 e. x1= 0, x2 9 Z=54 Page 7 of 19
43. Assume that we are using 0-1 integer programming model to solve a capital budgeting problem and xj = 1 if project j is selected and xj= 0, otherwise. The constraint (x1 + x2 + x3+ x4 2) means that out of the projects must be selected. a. exactly 1, 4 b. exactly 2, 4 c. at least 2, 4 d. at most 2, 4 44. In a 0-1 integer programming model, if the constraint x1-x2 = 0, it means when project 1 is selected, project be selected. a. can also b. can sometimes c. can never d. must also 45. The Wiethoff Company has a contract to produce 10000 garden hoses for a customer. Wiethoff has 4 different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same. Machine Fixed cost to set up production run Variable cost per hose Capacity 1 750 1.25 6000 2 500 1.50 7500 3 1000 1.00 4000 4 300 2.00 5000 Write a constraint to ensure that if machine 4 is used, machine 1 will not be used. a. Y1+Y4 0 b.y1+y4=0 c.y1+y4 1 d. Y1 + Y4 0 e. y1+y4 1 46. The solution to the linear programming relaxation of a minimization problem will always be the value of the integer programming minimization problem. a. greater than or equal to b. less than or equal to c. equal to d. different than 47. Rounding large values of decision variables to the nearest integer value causes problems than rounding small values. a. similar b. more c. fewer d. none of the above 48. In a integer model, the solution values of the decision variables are 0 or 1. a. total b. binary c. mixed d. all of the above Page 8 of 19
49. Which of the following correctly describes the focus of the Critical Path Method? a. To order activities in a project in terms of their completion time to facilitate scheduling of the activities. b. To determine when a project should be completed and to schedule when each activity in the project must begin in order to keep the project on schedule. c. To estimate the probability of completing a project by a given deadline when the time required to perform the activity is essentially a random variable. d. To structure the activities of a project in order to eliminate or reduce critical. dependencies among the activities. 50. The term time zero identifies a. the start time for each activity. b. the start time for the project. c. midnight on each work day. d. days with not wasted effort. (Items #51 - #61) Newfoundland Steel Corporation [NSC] produces four sizes of steel I-beams: small, medium, large, and extra large. These beams can be produced on any of three machines: A, B, and C. The lengths in feet of the I beams that can be produced on the machines per hour are as follows: I-Beam Machine Size A B C Small 300 600 800 Medium 250 400 700 Large 200 350 600 Extra Large 100 200 300 Each machine can be used up to 40 hours per week, and hourly operating costs of machines A, B, and C are $30.00, $50.00, and $80.00, respectively. Weekly requirements of the different sizes of I beams are, respectively, 10,000, 8,000, 6,000, and 6,000 feet. An analyst has formulated an LP model for this machine scheduling problem, defining the decision variables as follows: tjk = number of hours per week that machine j is used to produce I beams of size k with j = A, B, C and k = S (small), M (medium), L (large), E (extra large). Newfoundland Steel Corporation Minimize 30 TAS + 30 TAM + 30 TAL + 30 TAE + 50 TBS + 50 TBM + 50 TBL + 50 TBE + 80 TCS + 80 TCM + 80TCL + 80 TCE S.T. 1) 1TAS+1TAM+1TAL+1TAE 40 [Machine A hours per week] 2) 1TBS+1TBM+1TBL+1TBE 40 [Machine B hours per week] 3) 1TCS+1TCM+1TCL+1TCE 40 [Machine C hours per week] 4) 300TAS+600TBS+800TCS 10000 [Weekly demand for small I-beams (in feet)] 5) 250TAM+400TBM+700TCM 8000[Weekly demand for medium I-beams (in feet)] 6) 200TAL+350TBL+600TCL 6000 [Weekly demand for large I-beams (in feet)] 7) 100TAE+200TBE+300TCE 6000 [Weekly demand for extra large I-beams (in feet)] Page 9 of 19
Computer Output: OPTIMAL SOLUTION Objective Function Value = 4069.841 Variable Value Reduced Costs -------------- --------------- ------------------ TAS 0.000 3.333 TAM 0.000 1.429 TAL 0.000 3.333 TAE 0.000 3.333 TBS 16.667 0.000 TBM 0.000 7.619 TBL 0.000 6.667 TBE 23.333 0.000 TCS 0.000 8.889 TCM 11.429 0.000 TCL 10.000 0.000 TCE 4.444 0.000 Constraint Slack/Surplus Dual Prices -------------- --------------- ------------------ 1 40.000 0.000 2 0.000 3.333 3 14.127 0.000 4 0.000-0.089 5 0.000-0.114 6 0.000-0.133 7 0.000-0.267 OBJECTIVE COEFFICIENT RANGES Variable Lower Limit Current Value Upper Limit ------------ --------------- --------------- --------------- TAS 26.667 30.000 No Upper Limit TAM 28.571 30.000 No Upper Limit TAL 26.667 30.000 No Upper Limit TAE 26.667 30.000 No Upper Limit TBS -3.333 50.000 56.667 TBM 42.381 50.000 No Upper Limit TBL 43.333 50.000 No Upper Limit TBE 43.333 50.000 53.333 TCS 71.111 80.000 No Upper Limit TCM 0.000 80.000 84.000 TCL 0.000 80.000 90.000 TCE 75.000 80.000 90.000 RIGHT HAND SIDE RANGES Constraint Lower Limit Current Value Upper Limit ------------ --------------- --------------- --------------- 1 0.000 40.000 No Upper Limit 2 18.810 40.000 46.667 3 25.873 40.000 No Upper Limit 4 6000.000 10000.000 22714.286 5 0.000 8000.000 17888.889 6 0.000 6000.000 14476.190 7 4666.667 6000.000 10238.095 Page 10 of 19
51. The given LP model A. may be solved using the graphical method of linear programming B. may be solved using a computer software (e.g. Excel and The Management Scientist) C. Both A and B D. Neither A nor B 52. For the LP to be written in standard form, slack variables will be needed in how many of the constraints? A. None of the constraints B. 3 C. 4 D. All technical constraints 53. For the LP model to be written in standard form, surplus variables will be needed in which constraints? A. None of the constraints B. 1) through 3) C. 4) through 7) D. 1) through 7) 54. Which of the following is an appropriate interpretation (in the language of the problem) of the value of t BE in the optimal solution reported in the Storm output? A) Produce approximately 23 feet of extra large I-beams on machine B per week. B. Produce approximately 4,667 feet of extra large I-beams on machine B per week. C. Produce approximately 23,333 feet of extra large I-beams on machine B per week. D. Produce extra large I-beams on machine B for 23 hours and 20 minutes per week. 55. At the reported optimal solution, which constraints are NOT binding? A. None B Constraints 1) and 3) C. Constraints 2), 4), 5), 6), 7) D. All technical constraints 56. The "slack variable" value of 14.1270 reported for constraint 3) means A. machine C will be fully utilized. B. machine C will not be used at all. C.machine C will have underutilized capacity. D. none of the above. 57. The "slack variable" value of 40.0000 reported for constraint 1) means A. machine A will be fully utilized. B. machine A will not be used at all. C. machine A will have underutilized capacity. D. none of the above. 58. If the capacity of machine B were to be increased to 44 hours, then the optimal total machine operating cost per week would change by what amount? A. increase by about $3.33 B. decrease by about $3.33 C. increase by about $13.33 D. decrease by about $13.33 E. not change Page 11 of 19
59. If the capacity of machine C were to be increased to 44 hours, then the optimal total machine operating cost per week would change by what amount? A. increase by about $3.33 B. decrease by about $3.33 C. increase by about $13.33 D. decrease by about $13.33 E. not change 60. If the requirement for large sized I beams were to be increased to 7,000 feet, by how much would the optimal total machine operating cost per week change? A. not change B. increase by $133.3 C. decrease by $133.3 D. Cannot tell. Need to solve revised LP. 61. If the requirement for extra large sized I beams were to be increased to 11,000 feet, by how much would the optimal total machine operating cost per week change? A. not change B. increase by $1,333.5 C. decrease by $1,333.5 D. Cannot tell. Need to solve revised LP. Item #s 62 69. Comidas Norteamericano, a fast growing "Tex-Mex" food distribution company, is expanding into Ontario with the opening of two new sales territories Eastern Ontario and Western Ontario. Three individuals currently based in Chicago are being considered for appointment to regional sales manager positions in the new sales territories. Management has estimated total annual sales (in thousands of Canadian dollars) for the assignment of each individual to each sales territory. Top management's sales projections are as follows: Sales Region Sales Manager Eastern Ontario Western Ontario Aguirre $100 $95 Marin $85 $80 Reza $90 $75 62. Which of the following best specifies the decision variables for this problem? A. xj = annual sales (in $000) in sales region j B. xi = annual sales (in $000) by sales manager i C. xij annual sales (in $000) by sales manager i in sales region j D. xij= 1, if sales manager i is assigned to sales region j. 0, otherwise E. None of the above 63. The appropriate number of decision variables for this problem is A. two B. three C. five D. six E. none of the above Page 12 of 19
64. Which of the following best specifies the objective for this problem? A. Min si xi B. Max sj xj. C. Min i jsijxij D. Max i jsijxij E. None of the above 65. The given problem may be solved using which of the following mathematical programming models? A. assignment model only B. assignment or integer programming model only C. assignment or transportation model only D. any of assignment, transportation, or integer programming models 66. Which of the following would constitute an appropriate constraint for the mathematical model? A. x ME + x MW = 1 B. x AE + x AW 1 C. x RE + x RW 1 D. x ME + x MW = 2 E. None of the above 67. Given a situation where three products, each of which requires setting up manufacturing process equipment, may be produced. Product i involves a fixed setup cost of Ci, while each unit of product i yields a contribution margin of pi dollars per unit. The objective is to maximize total contribution margin net of fixed setup cost. The best set of decision variables for this problem would be A. all binary variables B. all nonnegative, integer variables C. mix of nonnegative, integer variables and binary variables D. all nonnegative variables E. none of the above 68. In #67, a maximum of 200 units may be produced if the manufacturing process equipment is set up for product 2. Which of the following would best specify the constraint associated with this given information (after decision variables are properly defined)? A. x 2 200 B. x 2 200y 2 C. x 2 200 D. x 2 200y 2 69. Which of the following would best specify the objective for the decision model for #6 (after decision variables are properly defined)? Page 13 of 19
70. Which of the following is true regarding projects? a. Projects can have a unique start activity and a unique finish activity. b. Projects can have multiple start activities and a unique finish activity. c. Projects can have multiple start and finish activities. d. All the above are true regarding projects. 71. Slack represents the amount of time by which an activity can be delayed without delaying the entire project, assuming that a. all successor activities start at their earliest start times. b. all predecessor activities start at their earliest start times. c. immediate predecessor activities start at their earliest start times. d. all predecessor activities start at their latest start times. 72. The purpose of the forward pass in the Critical Path Method technique is to a. Review each of the precedence relationships in the activity network. b. To calculate the slack time within each node on the activity network. c. To determine the earliest time each activity can start and finish. d. To determine the latest time each activity can start and finish. 73. The purpose of the backward pass in the Critical Path Method technique is to a. Review each of the precedence relationships in the activity network. b. To calculate the slack time within each node on the activity network, c. To determine the earliest time each activity can start and finish. d. determine the latest time each activity can start and finish. 74. Activities following a node a. can begin as soon as any activity preceding the node has been completed. b. have an earliest start time equal to the largest of the earliest finish times for all activities entering the node. c. have a latest start time equal to the largest of the earliest finish times for all activities entering the node. d. None of the alternatives is correct. 75. Activities G, P, and R are the immediate predecessors for activity W. If the earliest finish times for the three are 12, 15, and 10, then the earliest start time for W a. is 10. b. is 12. c. is 15. d. cannot be determined. 76. Activities K, M and S immediately follow activity. H, and their latest start times are 14, 18, and 11. The latest finish time for activity H a. is 11. b. is 14. c. is 18. d. cannot be determined. Page 14 of 19
77. Slack equals a. LF EF. b. EF LF. c. EF LS. d. LF ES. 78. Project management differs from management for more traditional day-to-day activities of a firm mainly because of a. it has limited time frame b. its unique set of activities c. a and b d. none of the above 79. activities cannot share the same start and end notes. a. 2 or more b.3 or more c. 4 or more d. 5 or more 80. If t is the expected completion time for a given activity, then a. LF = LS - t b. E F = ES - t c. EF = ES + t d. EF = LS - ES 81. The LS and LF are calculated using the a. backward pass through the network b. forward pass through the network c. values for ES and EF d. backward and forward pass through the network 82. Given the following information for a project, determine the critical path. a. A-C-E-H b. B-C-E-H c. B-D-F-H d. B-D-G-H 83. Given the information for the project in #82, determine the estimated completion time of the project. a. 23 days Page 15 of 19
b. 19 days c. 22 days d. 25 days 84. In a mixed integer model, all decision variables have integer solution values. 85. In a mixed integer model, the solution values of the decision variables are 0 or 1. 86. The solution value (Z) to the linear programming relaxation of a minimization problem will always be less than or equal to the optimal solution value (Z) of the integer programming minimization problem 87. The solution value (Z) to the linear programming relaxation of a maximization problem will always be less than or equal to the optimal solution value (Z) of the integer programming maximization problem 88. Rounding non-integer solution values up to the nearest integer value can result in an infeasible solution to an integer programming problem. 89. A path through a project network must reach every node. 90. The latest finish time for an activity is the largest of the latest start times for all activities that immediately follow the activity. 91. The earliest start time for an activity is equal to the smallest of the earliest finish times for all its immediate predecessors. a. T rue 92. A precedence relationship shows the sequence of activities in a project. 93. When earliest finish is subtracted from latest finish, we obtain the slack value for the activity Page 16 of 19
94. The earliest finish time for the final activity on a project network is also the total completion of the project. 95. The integer programming model for a transportation problem has constraints for supply at each source and demand at each destination. 96. A multiple regression model should always be used over a simple regression model: Questions #97 and #98 The scatterplots below pertain to Questions #97 and #98. 97. The sample coefficient of correlation between variable Y and variable X associated with each scatterplot is calculated and denoted by r A, r B, r C, and r D respectively. Which of the following statements is true? Page 17 of 19
99. A condition that exists when two or more independent variables are correlated with one another is called: a. autocorrelation. b. heteroscedasticity. c. non-normality. d. multicolinearity. 100. To test the validity of a multiple regression model involving two independent variables, the null hypothesis is that Page 18 of 19
* ANSWER KEY 1D 21 C 41A 61D 81 A 2E 22 D 42D 62D 82 B 3B 23 C 43D 63D 83 D 4D 24 B 44D 64D 84 B 5C 25 B 45C 65C 85 B 6A 26 A 46B 66B 86 A 7C 27 D 47C 67C 87 B 8B 28 D 48B 68B 88 A 9B 29 C 49B 69D 89 B 10C 30 D 50B 70C 90 B 11A 31 B 51B 71D 91 B 12D 32 A 52B 72C 92 A 13B 33 D 53C 73D 93 A 14D 34 B 54D 74B 94 A 15B 35 A 55B 75C 95 A 16B 36 C 56C 76A 96 B 17C 37 D 57B 77A 97 A 18B 38 C 58D 78C 98 C 19D 39 C 59E 79A 99 D 20A 40 D 60B 80C 100 D Page 19 of 19