**SAINT GB334 FINAL EXAM**

Question 1. 1.In a PERT network, the earliest (activity) start time is the: (Points : 2)

earliest time that an activity can be finished without delaying the entire project

latest time that an activity can be started without delaying the entire project

earliest time that an activity can start without violation of precedence requirements

latest time that an activity can be finished without delaying the entire project

none of the above

Question 2. 2.Given an activity's optimistic, most likely, and pessimistic time estimates of 4, 12, and 18 days respectively, what is the PERT variance for this activity? (Points : 2)

2.33

5.44

8.00

64.00

None of the above

Question 3. 3.The expected time in PERT is: (Points : 2)

a weighted average of the most optimistic time, most pessimistic time, and four times the most likely time

the modal time of a beta distribution

a simple average of the most optimistic, most likely, and most pessimistic times

the square root of the sum of the variances of the activities on the critical path

none of the above

Question 4. 4.According to the table below, there are five activities in a PERT project.

Click here to view a Word version of the table.

Using the data in the table, if the normal distribution were used to find the probability of finishing this project in 24 weeks or fewer, what mean and variance respectively would be used?

(Points : 2)

20; 4.222

30; 5.222

20; 5.222

30; 4.222

22.667; 1.111

Question 5. 5.The following table represents a project with four activities. All times are in weeks.

Click here to view a Word version of the table.

Using the data in the table, what is the critical path?

(Points : 2)

A-B

A-C

B-D

A-B-C-D

None of the above

Question 6. 6.Bank Boston has a branch at Bryant College. The branch is busiest at the beginning of the college year when freshmen and transfer students open accounts. This year, freshmen arrived at the office at a rate of 40 per day (assume 8-hour days). On average, it takes the Bank Boston staff person about ten minutes to process each account application. The bank is considering having one or two tellers. Each teller is paid $12 per hour and the cost of waiting in line is assumed to be $8 per hour.

What is the average number of people waiting to open accounts? (Points : 2)

3.27

4.16

5.27

5.83

Question 7. 7.A suburban specialty restaurant has developed a single drive-thru window. Customers order, pay, and pick up their food at the same window. Arrivals follow a Poisson distribution while service times follow an exponential distribution. If the average number of arrivals is 6 per hour and the service rate is 2 every 15 minutes, how much time will elapse (in hours) from the time a customer enters the line until he/she leaves the restaurant? (Points : 2)

0.50

0.25

0.75

2.25

3.00

Question 8. 8.A widely used mathematical programming technique designed to help managers and decision making relative to resource allocation is called __________. (Points : 2)

linear programming

computer programming

constraint programming

goal programming

None of the above

Question 9. 9.Consider the following linear programming problem:

Maximize 12X + 10Y

Subject to:

4X + 3Y ? 480

2X + 3Y ? 360

all variables ? 0

The maximum possible value for the objective function is __________. (Points:2)

360

480

1,520

1,560

none of the above

Question 10. 10.If items being transported must go through an intermediate point before reaching a final destination, then this situation is known as a(n) __________. (Points : 2)

transshipment problem

assignment problem

transportation problem

intermediate point problem

None of the above

Question 11. 11.Which of the following is not a popular definition of quality? (Points : 2)

Quality is the totality of features and characteristics of a product or service that bears on its ability to satisfy stated or implied needs.

Quality is defined as a competitively priced product that surpasses customer needs.

Quality is the degree to which a product conforms to design or specification.

Quality is fitness for use.

Even though quality cannot be defined, you know what it is.

Question 12. 12.Variations that usually occur in a process are called __________. (Points : 2)

process variations

natural variations

control variations

assignable variations

none of the above

Question 13. 13.A feasible solution to a linear programming problem: (Points : 2)

must be a corner point of the feasible region.

must satisfy all of the problem’s constraints simultaneously.

need not satisfy all of the constraints, only the non-negativity constraints.

must give the maximum possible profit.

must give the minimum possible cost.

Question 14. 14.Click here to view a Word version of the table.

To guarantee that cans of soup are properly filled, some cans are sampled and the amounts measured. The overall average for the samples is 12 ounces. Each sample contains 10 cans. The average range is 0.4 ounces.

Using the data in the table above, what is the lower control chart limit for the sample averages? (Points : 2)

12.1232

11.8768

13.2

12.308

None of the above

Question 15. 15.Which of the following control charts is/are for attributes? (Points : 2)

p-chart

x-bar chart

R-chart

A and B

A, B, and C

Question 16. 16.A certain firm has four different operations that must be assigned to four locations. The profit (in thousands of dollars) associated with each operation at each location is presented below. The firm’s vice president would like to assign the various operations so that the total profit is maximized. Find the appropriate assignments.

Click here to view an Excel version of the table.

Using the data in the table, what is the optimal location for Operation Z? (Points : 2)

1

2

3

4

Question 17. 17.Given the table below, the final table for an assignment problem, who should be assigned to Job 2?

Click here to view an Excel version of the table.

(Points : 2)

Worker A

Worker C

Either worker A or worker C

Neither worker A nor worker C

Worker D

Question 18. 18.A company believes a process monitored by an x-bar chart to be in control. When the most recent control point exceeded the UCL value by 20%, the company should: (Points : 2)

believe that a random bad luck chance occurred and proceed.

suspect that an assignable cause of variation now exists and can be found.

ignore the control point completely, as it is simply an outlier.

wait for the next four samples to be taken to see if a trend develops.

none of the above.

Question 19. 19.Click here to view a Word version of the table.

Bags of chocolate candy are sampled to ensure proper weight. The overall average for the samples is 36 ounces. Each sample contains twelve bags. The average range is 1.3 ounces.

Using the data in the table above, what is the lower control chart limit for the sample averages? (Points : 2)

36.3730

36.4849

35.6270

35.5150

Question 20. 20.Consider the following linear programming model:

Minimize 2X1 + 3X2

Subject to:

X1 + X2 ? 4

X1 ? 2

X1, X2 ? 0

This linear programming model has: (Points : 2)

a unique optimal solution.

an unbounded solution.

an infeasible solution.

an alternate optimal solution.

redundant constraints.

Question 21. 21.When using the shortest-route technique, the second step is to: (Points : 2)

find the next-nearest node to the origin and put the distance in a box by the node.

trace the path from the warehouse to the plant.

determine the average distance traveled from source to end.

find the nearest node to the origin and put a distance box by the node.

None of the above is correct.

Question 22. 22.The shortest-route technique would best be used to: (Points : 2)

assign workers to jobs in the cheapest manner.

determine the number of units to ship from each source to each destination.

determine the amount of LAN network wiring within a building.

minimize the amount of traffic flow on a busy highway.

determine the path for a truck making frequent but repeatable drops.

Question 23. 23.The p-chart is useful when we: (Points : 2)

take a number of measurements and compute the average.

take a number of measurements and compute the ranges.

find the fraction of the production lot defective.

find the number of defective items in a production lot.

None of the above is correct.

Question 24. 24. A finite population model differs from an infinite population model because there is a random relationship between the length of the queue and the arrival rate. (Points : 2)

True

False

Question 25. 25.The wait time for a single-channel system is more than twice that for a two-channel system using two servers working at the same rate as the single server. (Points : 2)

True

False

Question 26. 26.The maximal-flow technique finds the maximum flow of any quantity or substance through a network. (Points : 2)

True

False

Question 27. 27.Two characteristics of arrivals are the line length and queue discipline. (Points : 2)

True

False

Question 28. 28.The points on the network are referred to as nodes. (Points : 2)

True

False

Question 29. 29.In the maximal-flow technique, a zero (0) means no flow or a one-way arc. (Points : 2)

True

False

Question 30. 30.Infeasibility in a linear programming problem occurs when: (Points : 2)

there is an infinite solution.

a constraint is redundant.

more than one solution is optimal.

the feasible region is unbounded.

there is no solution that satisfies all the constraints given.

Question 31. 31. A certain firm has four different operations that must be assigned to four locations. The profit (in thousands of dollars) associated with each operation at each location is presented below. The firm’s vice president would like to assign the various operations so that the total profit is maximized. Find the appropriate assignments.

Click here to view an Excel version of the table.

Using the data in the table, what is the optimal location for Operation W? (Points : 2)

1

2

3

4

Question 32. 32.In a single-channel, single-phase system, reducing the service time only reduces the total amount of time spent in the system, not the time spent in the queue. (Points : 2)

True

False

Question 33. 33.A company can decide how many additional labor hours to acquire for a given week. Subcontractor workers will only work a maximum of 20 hours a week. The company must produce at least 200 units of product A, 300 units of product B, and 400 units of product C. In 1 hour of work, worker 1 can produce 15 units of product A, 10 units of product B, and 30 units of product C. Worker 2 can produce 5 units of product A, 20 units of product B, and 35 units of product C. Worker 3 can produce 20 units of product A, 15 units of product B, and 25 units of product C. Worker 1 demands a salary of $50/hr, worker 2 demands a salary of $40/hr, and worker 3 demands a salary of $45/hr. The company must choose how many hours they should contract with each worker to meet their production requirements and minimize labor cost.

Assuming this is a linear programming problem, which of the following is the optimal solution? (Points : 2)

X1 = 7.69; X2 = 0; X3 = 9.23

X1 = 0; X2 = 7.69; X3 = 9.23

X1 = 0; X2 = 9.23; X3 = 7.69

X1 = 9.23; X2 = 7.69; X3 = 0

Question 34. 34.A company must assign mechanics to each of four jobs.

Click here to view an Excel version of the table.

The time involved varies according to individual abilities. The table shows how many minutes it takes each mechanic to perform each job. If the optimal assignments are made, how many total minutes would be required for completing the jobs? (Points : 2)

0

4

17

16

None of the above

Question 35. 35.The customer who arrives at a bank, sees a long line, and leaves to return another time is __________. (Points : 2)

balking

cropping

reneging

blithering

none of the above.

uestion 36. 36.Two models of a product — Regular (X) and Deluxe (Y) — are produced by a company. A linear programming model is used to determine the production schedule. The formulation is as follows:

Maximize profit = 50X + 60Y

Subject to:

8X + 10Y ? 800 (labor hours)

X + Y ? 120 (total units demanded)

4X = 5Y ? 500 (raw materials)

all variables ? 0

The optimal solution is X = 100, Y = 0.

How many units of the regular model would be produced based on this solution? (Points : 2)

0

100

50

120

None of the above

Question 37. 37.In PERT, we assume that: (Points : 2)

the times to complete individual activities are known with certainty.

all activities are carried out by staff from our own organization.

the total cost of a project is independent of the time to complete the project.

the total time to complete all activities on the critical path is described by a normal distribution.

none of the above.

Question 38. 38.The difference between the left-hand side and right-hand side of a greater-than-or-equal-to constraint is referred to as __________. (Points : 2)

surplus

constraint

slack

shadow price

none of the above

Question 39. 39.A suburban specialty restaurant has developed a single drive-thru window. Customers order, pay, and pick up their food at the same window. Arrivals follow a Poisson distribution while service times follow an exponential distribution. If the average number of arrivals is 6 per hour and the service rate is 2 every 15 minutes, what proportion of the time is the server busy? (Points : 2)

0.25

0.50

0.75

2.25

3.00

Question 40. 40.Which of the following is not an assumption of LP? (Points : 2)

Simultaneity

Certainty

Proportionality

Divisibility

Additivity

Question 41. 41.Practically speaking, multiple optimal solutions __________. (Points : 2)

are infeasible

are unbounded

are degenerate

are unbalanced

provide management with greater flexibility in selecting and using resources

Question 42. 42.Cars arrive at a local JLUBE franchise at the rate of 1 every 12 minutes. Service times are exponentially distributed with an average of 15 minutes. Jack Burns, the JLUBE owner, has decided to open a second work bay, i.e., make the shop into a two-channel system. Under this new scheme, the total time an average customer spends in the system will be (Points : 2)

37 minutes.

2.1 minutes.

9.6 minutes.

33.3 minutes.

24.6 minutes.

Question 43. 43.An automatic car wash is an example of a constant service time model. (Points : 2)

True

False

Question 44. 44.Customers enter the waiting line to pay for food as they leave a cafeteria on a first-come, first-served basis. The arrival rate follows a Poisson distribution, while service times follow an exponential distribution. If the average number of arrivals is four per minute and the average service rate of a single server is seven per minute, on average, how much time will elapse from the time a customer enters the line until he/she leaves the cafeteria? (Points : 2)

0.67 minute

0.50 minute

0.75 minute

0.33 minute

1.33 minutes

Question 45. 45.A certain firm has four different operations that must be assigned to four locations. The profit (in thousands of dollars) associated with each operation at each location is presented below. The firm’s vice president would like to assign the various operations so that the total profit is maximized. Find the appropriate assignments.

Click here to view an Excel version of the table.

Using the data in the table, what is the optimal location for Operation X? (Points : 2)

1

2

3

4

Question 46. 46.Which of the following is not a property of all linear programming problems? (Points : 2)

The presence of restrictions

Optimization of some objective

A computer program

Alternate courses of action to choose from

Usage of only linear equations and inequalities

Question 47. 47.Typical resources of an organization include __________. (Points : 2)

machinery usage

labor volume

warehouse space utilization

raw material usage

all of the above

Question 48. 48.Assume that we are using a waiting line model to analyze the number of service technicians required to maintain machines in a factory. Our goal should be to: (Points : 2)

maximize productivity of the technicians.

minimize the number of machines needing repair.

minimize the downtime for individual machines.

minimize the percent of idle time of the technicians.

minimize the total cost (cost of maintenance plus cost of downtime).

Question 49. 49.The shortest-route technique might be logically used for: (Points : 2)

finding the longest time to travel between two points.

finding the shortest travel distance between two points.

finding the most scenic route to allow travel to several places during a trip on spring break.

connecting all the points of a network together while minimizing the distance between them.

none of the above.

Question 50. 50.The c-chart is useful when we: (Points : 2)

take a number of measurements and compute the average.

take a number of measurements and compute the ranges.

find the fraction of the production lot defective.

find the number of defective items in a production lot.

None of the above is correct

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