5242 PRACTICE FINAL

Spring 2000

Information Systems and Quantitative Sciences, College of Business. Texas Tech University, Page 1

This exam consists of multiple choice questions and two exercises. The multiple-choice questions are worth 70% of the exam grade. Place your answers on the accompanying computerized answer sheet. Be certain to record your name on this exam as well as on the answer sheet.

1. Integer programming models are used to characterize

  1. knapsack loading problems.
  2. fixed charge problems
  3. capital budgeting problems
  4. all of these.
  5. a and c only

2. Compared with standard linear programming algorithms, those for treating integer linear programming problems usually are:

  1. less complex, due to fewer possible solutions
  2. less amenable to “what if” and sensitivity analysis
  3. always heuristic
  4. easier to formulate, simplier

3. When imposing integer variables to an otherwise standard linear programming problem,

  1. rounding down a non-integer solution will always give a feasible solution to the integer model
  2. round up a non-integer solution will always give an infeasible solution to the integer model
  3. round off a non-integer solution will always give an optimal solution to the integer model
  4. none of these

4. The optimal value of the objective function to a standard linear programming model with a maximization objective is 675. If integer restrictions are now imposed on the decision variables, one can be sure that the optimal value of

objective function to the integer model will:

  1. be greater than 675
  2. equal 675
  3. not exceed 675
  4. not be less than 675

LINEAR PROGRAMMING

Use the following output for questions 5 through 10

min 4x1+5x2+6x3

S.T.

1) x1+x2+x3<85

2) 3x1+4x2+2x3>280

3) 2x1+4x2+4x3>320

Obj. Function Value = 400.000000

Variable Value Reduced Costs

------

X1 0.000000 1.500000

X2 0.000000 3.000000

X3 80.000000 0.000000

Constraint Slack/Surplus Shadow Prices

------

1 5.000000 0.000000

2 0.000000 1.250000

3 40.000000 0.000000

OBJECTIVE COEFFICIENT RANGES

Variable Lower Current Upper

Limit Value Limit

X1 2.500000 4.000000 No Limit

X2 2.000000 5.000000 10.00000

X3 5.000000 6.000000 No Limit

RIGHT HAND SIDE RANGES

Constraint Lower Current Upper

Limit ValueLimit

------

1 80.000000 85.000000 No Limit

2 No Limit 280.000000 320.000000

3 280.000000 320.000000 360.000000

5. What variables make up the non-basis?

  1. X1, X2, X3
  2. S1, S2, S3
  3. X2, S2, X3
  4. X1, X2, S2
  5. X2, S1, S2

6. Which constraints are non-binding?

  1. 1, 2, 3
  2. 2, 3
  3. 3 only
  4. 1 and 3
  5. 1 and 2

7. If the obj. fcn. coefficient associated with X3 were reduced from 6 to 5.02 what would happen?

  1. Nothing.
  2. Basis change: X3 would enter the basis.
  3. Basis change: X3 would exit the basis.
  4. The obj. function value would increase.
  5. The obj. function value would decrease.

8. Which of the following statements is NOT true?

a. A feasible solution satisfies all constraints.

b. An optimal solution satisfies all constraints.

c. An infeasible solution violates all constraints.

d. A feasible solution point does not have to lie on the boundary of the feasible region.

9. If the RHS associated with constraint 2 were increased from its present value of 280 to 300 what would happen?

  1. Nothing
  2. Basis change
  3. No basis change, but basis variable values would change
  4. No basis change, but obj. fcn value at optimality would change

e. both c and d above

10. If the obj. function coefficient of X1 were reduced from its current value of 4 to 2

a. Nothing.

b. Basis change: X1 would enter the basis

c. Basis change: X1 would exit the basis

d. The obj function value would increase.

11. An over-constrained linear programming problem results in what type of solution?

a. Unbounded.

b. Degenerate

c. Infeasible.

d. Sub-optimal

12. A marketing research application uses the variable HD to represent the number of homeowners interviewed during the day. The objective function minimizes the cost of interviewing this and other categories and there is a constraint that HD >= 100. The solution indicates that interviewing another homeowner during the day will increase costs by 10.00. What do you know?

a. the obj. function coefficient of HD is 10.

b. the shadow price for the HD constraint is 10.

c. the obj. function coefficient of HD is -10.

d. the reduced cost for the HD constraint is -10.

13. The shadow price for a constraint that compares funds used with funds available is .058. This means that

a. the cost of additional funds is 5.8%.

b. if more funds can be obtained at a rate of 5.5%, some should be.

c. no more funds are needed.

d. the objective was to minimize.

14. Let CM = the number of components to make and CB = the number of components to buy. If no more than 3000 components are needed, then

a. CM - CB <= 3000

b. CM + CB <= 3000

c. CM - CB >= 3000

d. CM + CB = 3000

15. If xij = the production of product i in period j, then to indicate that the limit on production of 3 products in period 2 is 400,

a. x21 + x22 + x23 <= 400

b. x12 + x22 + x32 <= 400

c. x32 <= 400

d. x23 <= 400

16. The amount that the objective function coefficient of a decision variable would have to improve before that variable would become a basis variable and have a positive value in the solution is the

  1. shadow price.
  2. surplus variable.
  3. reduced cost.
  4. upper limit.
  5. constraint RHS

17. To find the optimal solution to a linear programming problem, move parallel objective function lines

a. out until the last feasible point is touched.

b. in until the last feasible point is touched.

c. in the direction of increasing values of the objective function.

d. in the direction of improving values of the objective function.

18. Slack

a. is the difference between the left and right sides of a constraint.

b. is the amount by which the left side of a <= constraint is smaller than the right side.

c. is the amount by which the left side of >= constraint is larger than the right side.

d. exists for each variable in a linear programming problem.

e. b and d only

19. A constraint with a positive slack value

a. will have a positive shadow price.

b. will have a negative shadow price.

c. will have a shadow price of zero.

d. has no restrictions for its shadow price.

20. The amount by which an objective function coefficient can change before a different set of values for the decision variables becomes optimal is the

a. optimal solution.

b. dual solution.

c. range of optimality.

d. range of in-feasibility.

21. A section of output from a computer-generated solution is shown here

Variable Lower Current Upper

Limit Value Limit

1 120 200 240

What will happen to the solution if the objective function coefficient for variable 1 increases by 20 from its current value of 200?

a. The value of the objective function will change, but the values of the decision variables and the shadow prices will remain the same.

b. The same decision variables will be positive, but their values, the objective function value, and the shadow prices will change.

c.. Nothing. The values of the decision variables, the shadow prices, and the objective function will all remain the same.

d. The problem will need to be resolved to find the new optimal solution and shadow price.

22. A section of output is shown here

Constraint Lower Current Upper

Limit Value Limit

2 240 300 420

What will happen if the right-hand-side for constraint 2 increases by 200?

  1. Nothing. The values of the decision variables, the shadow prices, and the objective function will all remain the same.
  2. The value of the objective function will change, but the values of the decision variables and the shadow prices will remain the same.
  3. The same decision variables will be positive, (same basis) but their values, the objective function value, and the shadow prices will change.
  4. The problem will need to be resolved to find the new optimal solution (new basis) and shadow price.

23. As the SIMPLEX proceeds from vertex to vertex

a. one non-basis variable enters the basis.

b. one basis variable is driven to zero.

c. the basis variables are solved in terms of the non-basis variables.

d. all of the above.

e. a and b only.

NETWORK PROGRAMMING

24. In the standard assignment problem where, for example, workers are being assigned tasks, which of the following situations would preclude the application of the assignment approach (the Hungarian algorithm)

  1. A worker may be assigned to more than one job
  2. A worker may be unable to perform a certain job
  3. The number of workers does not equal the number of jobs
  4. Workers may perform fractional parts of jobs.

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

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

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

c. a mixture of agents 1, 2, 3, and 4 will be assigned to 2 or less tasks.

d. there is no feasible solution.

26. In a standard transportation model, each objective function coefficient represents the:

a. total cost of shipping between a source to a destination node.

b. fixed cost of utilizing the route between a source and destination node.

c. unit cost of shipping from a source to a destination node.

d. negative "unit cost" of not using the route between a source and destination node.

27. In class we observed that network programming models such as the shortest route and minimal spanning tree are also integer programming models. We prefer to use particularized network algorithms rather than integer programming methods to solve these models because:

a. computer solutions are more accurate.

b. computer solutions are more reliable in the sense that the likelihood of getting an optimal solution at all is much better for large models.

c. computer solutions require less time and memory.

d. b and c only

28. The length of the shortest route (assuming a is the start node and f is the stop node) in the network shown above is

a. 8. d. 11.

b. 9.e. none of these

c. 10.

  1. The length of the minimal spanning tree for the network shown above is

a. 15.d. 21.

b. 17.

c. 27. e. none of these

  1. The shortest route through the network is

a. a—b—e—f d. a—c—e—f

  1. a—c—d—f
  2. a—b—d—fe. none of these
  1. The algorithm used to solve the minimal spanning tree problem is called the
  1. shortest route algorithm
  2. greedy algorithm
  3. Hungarian algorithm
  4. Simplex algorithm
  5. None of these
  1. LP models and NETWORK models possess feasible optimal solutions that are:
  1. on the interior of the feasible region.
  2. on the boundary of the feasible region.
  3. on the exterior of the feasible region.
  4. all of the above.
  5. a and b only.

DECISION MODELS

Problem 33 through 39 apply to the following situation: Office Complexes, Inc. must commit now on the number of office complexes it will construct during the fall of 1999. Sales are dependent on interest rates which are almost unpredictable at this point. OCI hypothesizes three possible interest scenarios. They are 9-10%, 10-11%, 11-13%. OCI has four possible acts to choose from—build no new complexes, build 10 complexes, build 20 complexes, or build 50 complexes, respectively. The associated payoff matrix is shown below. Payoffs are in thousands of dollars.

9-10%10-11%11-13%

a. 0 complexes 0 0 0

b. 10 complexes500200-100

c. 20 complexes900400-200

d. 50 complexes 3000 1000-2000

State Probabilities .4 .3 .3

33. What act should be employed if OCI is an optimist?

34. A pessimist?

35. A regrettist?

36. What is the optimal strategy under expected monetary value?

37. What is the expected return or payoff of perfect information?

a. 1200 b. 1400c. 1500

d. 900e. none of these

38. What is the expected value of perfect information?

a. 600 b. 1400c. 920

d. 3500e. none of these

39. What is the minimum expected regret?

a. 5300b. 600c. 3500

d. 800e. none of these

40. In decision models

a. the expected value of perfect information is always equal to the minimum expected regret.

b. the minimum expected regret act is always the same as the maximum expected payoff act.

c. the expected regret and the expected payoff associated with any act always sum to the same number

d. all of the above are true

e. none of the above are true.

41. When considering additional information,Bayesian revision is often necessary because

  1. conditional probabilities for predictive (or indicator) states are conditioned upon actual states
  2. marginal probabilities of the predictive states are unknown
  3. decision tree requires the probabilities of actual states conditioned upon predictive states
  4. all of the above
  5. none of the above

The marketing department of Production Unlimited, Inc., is considering whether or not to develop a new product. All the prior relevant information is shown in the table below.

Alternative / State / 0.6 / 0.4
of nature / Success / Failure
A1:DEVELOP / 1000000 / -700000
A2:DON’T / 0 / 0

42. Based on this prior information, which act should be chosen?

a. A2b. A1

A consultant can be hired to improve the information about the likelihood of the future states. For a fee off $50,000, the consultant can perform a market survey of a prototype of the product. The consultant’s conditional probabilities of prediction are

P(Sp/S) = .9P(Fp/F) = .8

Here Sp, and Fp are the consultant’s predicated states of nature based on market survey’s he has performed in the past and S, F are the actual states of nature. TO THE NEAREST 3 SIGNIFICANT DIGITS, WHAT ARE THE FOLLOWING?

43. What is P(Sp)?

a. .350b. .340

c. .480d. .620

  1. none of these

44. What is P(Fp)?

a. .650b. .660

c. .520d. .380

e. none of these

45. What is P(S/Sp)?

a. .871b. .533

c. .206d. .750

e. none of these

46. What is P(F/Sp)?

a. .129b. .467

c. .794d. .250

e. none of these

47. What is P(S/Fp)?

a. .158b. .201

  1. .077
  2. .035

e. none of these

48. What is P(F/Fp)?

a. .306b. .842

c. .993d. .254

e. none of these

49. Assuming the survey predicts outcome Sp, should the product be developed?

a. Yes

b. No

c. no way to determine-insufficient information

50. What is the expected value (not including the consultant’s fee) of developing the product assuming the survey predicts outcome Fp?

a. $-431,400b. $-218,000c. $-619,100d. $-63,400e. none of these

51. What is the expected value of developing the product assuming the survey predicts outcome Sp?

a. $286,000b. $651,300

c. $525,000d. $780,700e. $276,000

52. How much is the survey actually worth to Production Unlimited—i.e., the EVSI?

a. $356,409b. $164,034c. $989,143

d. $776,000e. none of these

53. How much would perfect information be valued to Production Unlimited, considering the payoff without any information? (Hint: subtract the EREV from the ERPI.)

a. $400,000b. $280,000c. $600,000

d. $230,110e. none of these

54. What is the optimal strategy?

a. Don’t hire consultant and introduce product directly.

b. Hire consultant and introduce product only if survey predicts Sp.

c. Hire consultant and introduce product only if survey predicts Fp.

d. Don’t hire consultant and don’t introduce product

e. none of these

MARKOV PROCESSES

55. In Markov analysis, we are concerned with the probability that the

a. state is part of a system.

b. system is in a particular state at a given time.

c. time has reached a steady state.

d. transition will occur.

56. If the probability of making a transition from a state to any other is 0, then that state is called a

a. steady state.

b. final state.

c. origin state.

d. absorbing state.

57. Markov processes have been used to

a. study how products in a market might compete for market share.

b. study how certain state probabilities might change over time.

c. study optimal risk decision strategies.

d. all of the above.

e. a and b above.

58. . | 0 1 0 0 |

| 0 .3 .6 .1 |

| 0 1 .5 .4 |

| 0 0 .7 .3 |

For the STM above, the steady-state probability for state 1 is”

  1. .63645
  2. .00000
  3. 1
  4. cannot be determined unless the initial state probabilities are given.

59. All of the following are necessary characteristics of a Markov process, except:

a. a countable number of stages.

b. a countable number of states, per stage.

c. at least one absorbing state.

d. the memoryless property.

60. This transition matrix represents what type of Markov process?

| 0.2 0.8 |

| 0 1 |

a. periodic

b. absorbing

c. independent

d. nonrecurrent

61. Regarding a transition matrix which possesses an absorbing state:

a. All row values will not sum to 1.

b. There will be a complementary absorbing state.

c. At least two columns will be identical.

d. That state's row will consist of a "1" and "0's".

CONTINUOUS SIMULATION

62. In continuous simulation models, there are two types of connectors between components. They are:

a. flows and stocks

b. information edges and flows

c. information edges and stocks

d. edges and information

63. Places where content can accumulate are called:

a. stocks or states

b. rates or derivatives

c. auxiliaries

d. outputs

64. A parameter is a quantity that has

a. no connectors directed toward it

b. no connectors directed away from it

c. no connectors at all

d. only flows directed away from it

65. The final destination of most information paths is

a. a state or stock

b. a rate

c. a parameter

d. an auxiliary

66. The only connector type that can be directed toward a state is

  1. a flow
  2. an information link
  3. both are acceptable

67. A flow connector must have

a. a rate associated with it

b. at least one state or stock associated with it

c. multiple destinations

  1. all of the above
  2. a and b only
  1. A population has a net growth rate normal of 3% a year. Its death rate normal is 2% a year. What is its birth rate normal?
  1. not determinable, not enough information
  2. 1% c. 4%

d. 5%e. 6%

  1. It is known that a death rate DR for a population is a function of the lifetime LT of the population and the size of the population P. The exact equation for death rate is:
  1. DR = (LT + 3*P)/4
  2. DR = LT + P
  3. DR = LT*P
  4. DR = P/LT
  5. None of these
  1. A pension FUND grows at the rate of 10% due to its investments. It is depleted by RETIREES who retire at half SALARY. On the other hand contributions replenish the fund as EMPLOYEES contribute 8% of their SALARY. How many rates deplete the stock pension fund?

a. 1 b. 2 c. 3 d. 4 e. none of these

  1. The equation for contributions to the fund is
  1. EMPLOYEES*SALARY*.08
  2. RETIREES*SALARY/2
  3. EMPLOYEES*FUND*.08
  4. EMPLOYEES*FUND/2
  5. None of these

The following questions involve your understanding of the program BLOCKS.

72. Which of these blocks will require that you specify a capacity in terms of number of

transactions?

a. CREATE/GENERATE

b. LEAVE/RELEASE

c. ADVANCE/ACTIVITY

d. BRANCH/TRANSFER

e. ENTER/SEIZE

73. In terms of the blocks listed in problem 72, which provides for a queue to build up in front of it?

74. Discrete simulations are used to model

a. waiting lines (queuing problems).

b. stochastic inventory problems.

c. continuous flows of people, goods,

money or material.

d. all of these.

e. a and b only.

75. Discrete simulation languages use all but which of the following as measures of performance:

  1. Average waiting time in a queue
  2. Population growth and decline
  3. Average utilization of a resource
  4. Average length of a queue.

76. Discrete simulations tend to be ______whereas continuous simulations, for the most

part, are ______.

a. nonlinear, linear

b. stochastic, deterministic

c. causal, correlative

d. transient steady state

e. descriptive, prescriptive

Build a model appropriate for BLOCKS to study the following problem. A large company cafeteria has three serving areas—hot food, sandwiches and drinks. Each area is to be modeled as a facility. The food is not free; there are three checkout stations, each with identical service statistics. Patrons arrive at the cafeteria at a rate that is exponential which mean of .2 minutes. Forty per cent of these customers choose the sandwich bar while only sixty per cent choose the hot meal counter. All customers then proceed to the self-serve drinks counter before moving into the cafeteria eating area, which has a capacity of 60 people. The time required for patrons to eat their meals is normal with a mean of 20 minutes and a standard deviation of five minutes. Service times for each of the serving areas, together with the number of servers are the following: (Hot food: Uniform with mean of 1 min. and +- bounds of .5 min and 4 servers.) (Sandwiches: exponential with a mean of .4 min. and 2 servers.) (Drinks: exponential with a mean of .3 minutes and 2 servers.) (The checkout stations have service times that are normal with a mean of 1 min. and a std. dev. of 1 min. and 3 servers.) The cafeteria manager is interested in the queue length and the average waiting time associated with each service facility. The manager is also interested in whether the eating area is large enough. No clock routine is needed.