cManagement Science Assignment
Question 1
The number of units expected to be sold is uniformly distributed between 300 and 500. If r is a random number between 0 and 1, then the proper expression for sales is
Select one:
a. 200(r)
b. r + 300
c. 300 + 500(r)
d. 300 + r(200)
Question 2
Question text
Greenfields is a mail order seed and plant business. The size of orders is uniformly distributed over the interval from $25 to $80. The following random numbers can be used to generate the size of 10 orders.
What is the value of the first order?
Select one:
a. 25
b. 80
c. 47.55
d. 22.55
Question 3
Question text
Simulation
Select one:
a. does not guarantee optimality.
b. is flexible and does not require the assumptions of theoretical models.
c. allows testing of the system without affecting the real system.
d. All of the alternatives are correct.
For the past 50 days, daily sales of laundry detergent in a large grocery store have been recorded (to the nearest 10).
Determine the relative frequency for sales of 40 units.
Select one:
a. 8
b. 50
c. .24
d. .16
Question 5
Question text
For the past 50 days, daily sales of laundry detergent in a large grocery store have been recorded (to the nearest 10).
Determine the interval of random numbers that can be used for sales of 40 units.
Select one:
a. 0 – .16
b. 0 – 8
c. 8 – 12
d. .16 – .40
Question 6
Question text
Using the frequency distribution from the previous question, suppose that the following random numbers were obtained using Excel.
Using these random numbers to simulate 10 days of sales, the first two days’ sales are:
Select one:
a. 30, 30
b. 12, 96
c. 40, 70
d. 30, 70
Question 7
Laurie Nomondy, a BBA student at OC, has been having problems balancing her cheque book. Her monthly income is derived from working as a lab demonstrator for several courses. In most months, she also makes extra money by tutoring first year business student in statistics. Her monthly expenses are normally distributed, with an average of $500 and a standard deviation of 50. In the following table her chances of various income levels are shown.
Using the spreadsheet shown, select the formula that would be found in each of the following cells. Make sure that the formula is in a form that will allow you to copy it for the column where appropriate.
The formula for the income calculation in cell B9 is:
Select one:
a. =VLOOKUP(RAND(),$A$2:$C$5,3)
b. =VLOOKUP(RAND(),A2:C5,3)
c. =NORMINV(RAND(),$E$2,$E$3)
d. =NORMINV(RAND(),E2,E3)
Question 8
Question text
The formula for the expenses calculation in cell C9 is:
Select one:
a. =VLOOKUP(RAND(),$A$2:$C$5,3)
b. =VLOOKUP(RAND(),A2:C5,3)
c. =NORMINV(RAND(),$E$2,$E$3)
d. =NORMINV(RAND(),E2,E3)
Question 9
Question text
The formula for the cash available in cell D9 is:
Select one:
a. =B9+C9
b. =$B$9+$C$9
c. = B9-C9
d. =$B$9-$C$9
Question 10
Question text
The formula for cell E9 is:
Select one:
a. =E8+B9+C9
b. =E8-D9
c. =$E$8+$D$9
d. =E8+D9
Question 11
Question text
The formula for cell E26 is:
Select one:
a. =MIN(E9:E23)
b. =MAX(E9:E23)
c. =MIN(D9:D23)
d. =MIN(C9:C23)
Question 12
Question text
The formula for cell E28 is:
Select one:
a. =STDEV(E9:E23)
b. =IF(X<300, THEN COUNT)
c. =COUNTIF(D9:D23,”<0″)
d. =COUNTIF(E9:E23,”<300″)
Question 13
Question text
The formula for cell E29 is:
Select one:
a. =E28/A23
b. =E28/E8
c. =E25/A23
d. =E28/E26
Your friend chose professional hockey instead of management science for a career, and he has asked you to figure out the probability he will score 30 goals or more this season, since he gets a bonus if he scores at least 30 goals. There are only five games remaining, and he has scored 25 goals so far. You decide to use simulation to answer his questions, and based on his past performance, you find the following probabilities:
Probability Goals Scored
0.64 0
0.3 1
0.05 2
0.01 3
Using Excel’s RAND() function, you generate the following random numbers for your simulation:
Random Numbers goal score
0.1 0
0.94 2
0.88 1
0.65 1
0.75 1
Using the random numbers you generated for each remaining game (in the order shown), simulate the goals scored by your friend in the remaining five hockey games, and answer the next two questions.
Question 14
Question text
How many goals will your friend score in game three of the five remaining games, according to your simulation?
Select one:
a. 0
b. 1
c. 2
d. 3
Question 15
Question text
How many goals will your friend score in total this season, according to your simulation?
Select one:
a. 30
b. 29
c. 28
d. 27
e. 26
Question 16
Question text
Joe Foodie wants to use Markov processing to analyze his weekly decision to dine at either an Italian or Mexican restaurant.
Select one:
a. the weekly visit is the trial and the restaurant is the state.
b. the weekly visit is the state and the restaurant is the trial.
c. the weekly visit is the trend and the restaurant is the transition.
d. the weekly visit is the transition and the restaurant is the trend.
17 If the probability of making a transition from a state is 0, then that state is called a(n)
Select one:
a. steady state.
b. final state.
c. origin state.
d. absorbing state
Question 18
Question text
Steady state probabilities are independent of initial state.
Select one:
a. True
b. False
Examination of past vehicle purchases in Lake Country has shown that the probability of a customer purchasing a vehicle from a given dealer is based on the customer’s previous purchase. In Lake Country, 1000 residents are expected to purchase autos in the next year. Use the following transition probabilities to answer the next 4 questions.
To
From Hundler Furdley Gumtoe Baemar
Hundler 0.8 .05 .05 .1
Furdley 0.2 .5 .1 .2
GumToe 0.2 .05 .6 .15
Baemar 0.1 .05 .05 .8
Question 19
Question text
Based on the above table, how many customers can Hundler expect to have in the long run?
Select one:
a. 384
b. 91
c. 404
d. 121
Question 20
Question text
Based on the above table, how many customers can Furdley expect to have in the long run?
Select one:
a. 384
b. 91
c. 404
d. 121
Question 21
Question text
Based on the above table, how many customers can Gumtoe expect to have in the long run?
Select one:
a. 384
b. 91
c. 404
d. 121
Question 22
Question text
Based on the above table, how many customers can Baemar expect to have in the long run?
Select one:
a. 384
b. 91
c. 404
d. 121
Markov Two airlines offer conveniently scheduled flights to the Kelowna airport. Historically, flights have been scheduled as reflected in this transition matrix.
If your last flight was on Okanagan Jet, what is the probability your next two flights will be on Air Okanagan?
Select one:
a. .7725
b. .24
c. .1125
d. .81
Question 24
Question text
Two airlines offer conveniently scheduled flights to the Kelowna airport. Historically, flights have been scheduled as reflected in this transition matrix.
If your last flight was on Okanagan Jet, what is the probability one of your next two flights will be on Okanagan Jet?
Select one:
a. .1650
b. .0375
c. .1275
d. .7225
Question 25
Question text
MarkOvRent-To-Keep rents household furnishings by the month. At the end of a rental month a customer can: a) rent the item for another month, b) buy the item, or c) return the item. The matrix below describes the month-to-month transition probabilities for 32-inch stereo televisions the shop stocks.
What is the probability that a customer who rented a TV this month will eventually return it?
Select one:
a. .357
b. .643 (The Answer Based on Moodle Review)
c. 1.00
d. .18
Question 26
Question text
Rent-To-Keep rents household furnishings by the month. At the end of a rental month a customer can: a) rent the item for another month, b) buy the item, or c) return the item. The matrix below describes the month-to-month transition probabilities for 32-inch stereo televisions the shop stocks.
The company currently has 75 customers renting household furnishings. How many of these will end up buying the furniture?75*0.357=26.775%
Select one:
a. 26.775 or 27 (The Answer based on Moodle Review)
b. .643
c. 13.5 or 14
d. 48.225 or 48
CN Rail specializes in transporting coal. On Friday, CN had empty freight cars at the following locations in the quantities indicated:
What is the minimum total distance over which cars are moved to new locations to meet demand?
Select one:
a. 2800
b. 3100
c. 6250
d. 9550
Question 28
Question text
Use your calculation for the CN Rail question to answer this question. In the optimal solution, is there a shipment from Truro to Coaltown?
Select one:
a. Yes
b. No
c. Can not be determined
Question 29
Question text
Use your calculation for the CN Rail question to answer this question. In the optimal solution, is there a shipment from Glace Bay to Coal Junction?
Select one:
a. Yes
b. No
c. Can not be determine
Question 30
Question text
Use your calculation for the CN Rail question to answer this question. Is all the demand being met?
Select one:
a. Yes
b. No
c. Can not be determined
Question 31
Question text
Use your calculation for the CN Rail question to answer this question. How many different locations supply Coaltown?
Select one:
a. 0
b. 1
c. 2
d. 3
e. Can not be determined
Question 32
Question text
Use your calculation for the CN Rail question to answer this question. Which supply location ships all its freight cars to only one demand location?
Select one:
a. Truro
b. New Bedford
c. Glace Bay
d. none of the above
Andrew Chilli, a stockbroker, has several recommendations for one of his clients. These recommendations can be found in the table below.
The client agrees to this list but provides several conditions:
1. no more than $3000 can be invested
2. at least five different investments must be purchased
3. no more than one type of bond can be purchased
4. at least two utility stocks must be purchased
5. at least two regular stocks must be purchased.
Formulate this as a 0-1 integer linear programming problem, using Ii for each investment, to help the client maximize expected return.
What is the objective function?
Select one:
a. Max I1 + I2 + I3 + I4 + I5 + I6 + I7 + I8
b. Max I1 + I2 + I3 + I4 + I5 + I6 + I7 + I8 = 3000
c. Max 500I1 + 1000I2 + 350I3 + 490I4 + 700I5 + 270I6 + 800I7 + 400I8
d. Max 50I1 + 100I2 + 30I3 + 45I4 + 65I5 + 20I6 + 90I7 + 35I8
Question 34
Question text
Andrew Chilli, a stockbroker, has several recommendations to a client. These recommendations can be found in the table below.
The client agrees to this list but provides several conditions:
1. no more than $3000 can be invested
2. at least five different investments must be purchased
3. no more than one type of bond can be purchased
4. at least two utility stocks must be purchased
5. at least two regular stocks must be purchased.
Formulate this as a 0-1 integer linear programming problem, using Ii for each investment, to help the client maximize expected return.
What is the equation for constraint one?
Select one:
a. I1 + I2 + I3 + I4 + I5 + I6 + I7 + I8 = 3000
b. I1 + I2 + I3 + I4 + I5 + I6 + I7 + I8 = 3000
c. 500I1 + 1000I2 + 350I3 + 490I4 + 700I5 + 270I6 + 800I7 + 400I8 = 3000
d. 50I1 + 100I2 + 30I3 + 45I4 + 65I5 + 20I6 + 90I7 + 35I8 = 3000
Question 35
Question text
Andrew Chilli, a stockbroker, has several recommendations to a client. These recommendations can be found in the table below.
The client agrees to this list but provides several conditions:
1. no more than $3000 can be invested
2. at least five different investments must be purchased
3. no more than one type of bond can be purchased
4. at least two utility stocks must be purchased
5. at least two regular stocks must be purchased.
Formulate this as a 0-1 integer linear programming problem, using Ii for each investment, to help the client maximize expected return.
What is the equation for constraint two?
Select one:
a. I1 + I2 + I3 + I4 + I5 + I6 + I7 + I8 = 5
b. I1 + I2 + I3 + I4 + I5 + I6 + I7 + I8 = 5
c. 500I1 + 1000I2 + 350I3 + 490I4 + 700I5 + 270I6 + 800I7 + 400I8 = 5
d. 50I1 + 100I2 + 30I3 + 45I4 + 65I5 + 20I6 + 90I7 + 35I8 = 5
Question 36
Question text
Andrew Chilli, a stockbroker, has several recommendations to a client. These recommendations can be found in the table below.
The client agrees to this list but provides several conditions:
1. no more than $3000 can be invested
2. at least five different investments must be purchased
3. no more than one type of bond can be purchased
4. at least two utility stocks must be purchased
5. at least two regular stocks must be purchased.
Formulate this as a 0-1 integer linear programming problem, using Ii for each investment, to help the client maximize expected return.
What is the equation for constraint three?
Select one:
a. I3 + I4 + I5 + I6 + I7 + I8 = 1
b. I1 + I2 = 1
c. I1 – I2 = 1
d. I1 – I2 = 0
Question 37
Question text
Andrew Chilli, a stockbroker, has several recommendations to a client. These recommendations can be found in the table below.
The client agrees to this list but provides several conditions:
1. no more than $3000 can be invested
2. at least five different investments must be purchased
3. no more than one type of bond can be purchased
4. at least two utility stocks must be purchased
5. at least two regular stocks must be purchased.
Formulate this as a 0-1 integer linear programming problem, using Ii for each investment, to help the client maximize expected return.
What is the equation for constraint four?
Select one:
a. I3 + I4 + I5 = 2
b. I3 + I4 + I5 = 2
c. I3 + I4 + I5 = 2
d. I3 – I4 – I5 = 0
Question 38
Question text
Andrew Chilli, a stockbroker, has several recommendations to a client. These recommendations can be found in the table below.
The client agrees to this list but provides several conditions:
1. no more than $3000 can be invested
2. at least five different investments must be purchased
3. no more than one type of bond can be purchased
4. at least two utility stocks must be purchased
5. at least two regular stocks must be purchased.
Formulate this as a 0-1 integer linear programming problem, using Ii for each investment, to help the client maximize expected return.
What is the equation for constraint five?
Select one:
a. I6 + I7 + I8 = 2
b. I6 + I7 + I8 = 2
c. I6 + I7 + I8 = 2
d. I6 – I7 – I8 = 0
Question 39
Question text
Andrew Chilli, a stockbroker, has several recommendations to a client. These recommendations can be found in the table below.
The client agrees to this list but provides several conditions:
1. no more than $3000 can be invested
2. at least five different investments must be purchased
3. no more than one type of bond can be purchased
4. at least two utility stocks must be purchased
5. at least two regular stocks must be purchased.
Formulate this as a 0-1 integer linear programming problem, using Ii for each investment, to help the client maximize expected return.
Solve the linear program. What is the optimal objective function value?
Select one:
a. 300
b. 290
c. 305
d. 285
Question 40
Question text (We need the table that defines the variables)
Using your solution for Andrew Chilli, should the client’s portfolio contain BC Bonds?
Select one:
a. Yes
b. No
c. Can not be determined
Question 41
Question textWe need the table that defines the variables
Using your solution for Andrew Chilli, should the client’s portfolio contain Nunavik Art Co?
Select one:
a. Yes
b. No
c. Can not be determined
Question 42
Question textWe need the table that defines the variables
Using your solution for Andrew Chilli, should the client’s portfolio contain PEI Electric?
Select one:
a. Yes
b. No
c. Can not be determined
Question 43
Consider the following transportation problem.
What would be the constraint for node 4?
Select one:
a. X14 + X24 + X34 < 500
b. – X14 – X24 – X34 + X46 + X47 = 0
c. – X14 – X24 – X34 + X46 + X47 < 0
d. – X14 – X24 – X34 + X15 + X25 + X35 = 0
Question 44
Question text
Arcs in a project network indicate
Select one:
a. completion times.
b. precedence relationships.
c. activities.
d. the critical path.
Question 45
Question text
The earliest start time rule
Select one:
a. compares the starting times of all activities for successors of an activity.
b. compares the finish times for all immediate predecessors of an activity.
c. determines when the project can begin.
d. determines when the project must begin.
Question 46
Question text
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
Select one:
a. is 11.
b. is 14.
c. is 18.
d. cannot be determined.
Slack equals= (Late Start – Early Start) OR (Late Finish – Early Finish)
Select one:
a. LF – EF.
b. EF – LF.
c. EF – LS.
d. LF – ES.
Question 48
Question text
If arrivals occur according to the Poisson distribution every 20 minutes, then which is NOT true?
Select one:
a. ? = 20 arrivals per hour
b. ? = 3 arrivals per hour
c. ? =1/20 arrivals per minute
d. ? =72 arrivals per day
Question 49
Question text
In a waiting line situation, arrivals occur, on average, every 10 minutes, and 10 units can be serviced every hour. What are and ?
Select one:
a. ? = 10, µ = 10
b. ? = 6, µ = 6
c. ? = 6, µ = 10
d. ? = 10, µ = 6 1 every 10 min & 60min/10= 6 per minute
Which of the following can NOT be found by the waiting line formulas presented in the textbook?
Select one:
a. the probability that no units are in the system.
b. the average number of units in the system.
c. the maximum time a unit spends in the system.
d. the average time a unit spends in the system.
Question 51
Question text
What queue discipline is assumed by the waiting line models presented in the textbook?
Select one:
a. first-come first-served.
b. last-in first-out.
c. shortest processing time first.
d. No discipline is assumed.
Question 52
Question text
The Kelowna Prestige Inn uses a toll-free telephone number to take reservations. The average time to handle each call is 3 minutes, and an average of 12 calls are received each hour. The probability distribution of the arrivals is unknown.
Over a period of time it is determined that the average caller spends 6 minutes in the system, waiting and receiving service.
Using Little’s Flow equations, what is the average time in minutes in the queue?
Select one:
a. 0.05
b. 0.92
c. 55
d. 3
Consider the following transportation problem.
What would be the constraint for node 4?
Question 53
Select one:
a. X14 + X24 + X34 < 500
b. – X14 – X24 – X34 + X46 + X47 = 0
c. – X14 – X24 – X34 + X46 + X47 < 0
d. – X14 – X24 – X34 + X15 + X25 + X35 = 0
Question text
The Kelowna Prestige Inn uses a toll-free telephone number to take reservations. The average time to handle each call is 3 minutes, and an average of 12 calls are received each hour. The probability distribution of the arrivals is unknown.
Question 44 Over a period of time it is determined that the average caller spends 6 minutes in the system, waiting and receiving service.
Question text
What is the average number in the queue?
Select one:
a. 72
b. 0.1
c. 0.6
d. 240
Select one:
Arcs in a project network indicate
a. completion times.
b. precedence relationships. Skip Quiz navigation
c. activities. Quiz navigation
d. the critical path.
Question 45
Question text
The earliest start time rule
Select one:
a. compares the starting times of all activities for successors of an activity.
b. compares the finish times for all immediate predecessors of an activity.
c. determines when the project can begin.
d. determines when the project must begin.
Question 46
Question text
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
Select one:
a. is 11.
b. is 14.
c. is 18.
d. cannot be determined.
The following network diagram represents a project plan for Okanagan Cycle, shown in precedence notation. The three PERT time estimates (in days) for each activity in the network are presented in the table below.
Use the standard PERT equations and assume that the total duration is normally distributed.
What is the expected total duration of the project?
Select one:
a. 81 days
b. 34 days
c. 110 days
d. 91 days
Question 55
Question text
Using your solution for Okanagan Cycle, what is the probability that the project will be completed in less than 100 days?
Select one:
a. 13.35%
b. 41.29%
c. 36.65%
d. 63.35%
Question 56
Question text
Using your solution for Okanagan Cycle, what is the probability of completing the project within the expected project completion time?
Select one:
a. 100%
b. Unknown
c. 75%
d. 50%
Question 57
Question text
Use your solution for Okanagan Cycle to answer this question. If the company wants a forecast completion date for which there is a 75% chance of meeting, what total duration should be used to determine the predicted completion date? Round to the nearest day.
Select one:
a. 116 days
b. 104 days
c. 83 days
d. 65 days
Hacky Sack recently purchased and now manages a ski and snowboard rental shop near Silver Star Ski Resort. As part of his due diligence prior to the purchase, he established that he should expect to get 20 customers per hour. From his previous work experience, Hacky figures he can serve up to 30 customers per hour. As such, he figures that it does not make sense for him to have any customer waiting lines.
Prior to the grand re-opening of his newly acquired rental shop, he wants to be certain of his assumptions about potential queues in his shop. In exchange for unlimited rentals, a local OC student (that’s you) agrees to examine the data and determine some characteristics of the potential queues. Assume Poisson arrivals and exponential service times.
What percent of time is Hacky busy serving customers?
Select one:
a. 0.067%
b. 33.33%
c. 10%
d. 66.67%
Question 59
Question text
Use your solution for Hacky Sack to answer this question. What is the average number of customers in the system?
Select one:
a. 2
b. 0.67
c. 1.33
d. 0.0667
Question 60
Question text
Use your solution for Hacky Sack to answer this question. What is the average number of minutes a customer spends in the system?
Select one:
a. 4.0
b. 0.100
c. 2.0
d. 6.0
Question 61
Question text
Use your solution for Hacky Sack to answer this question. What is the average number of minutes a customer spends in the queue waiting for service?
Select one:
a. 0.33
b. 0.0667
c. 1.33
d. 4.0
Question 62
Question text
Use your solution for Hacky Sack to answer this question. What is the average number of customers in the waiting line?
Select one:
a. 2
b. 1.33
c. 6
d. 0.10
Question 63
Question text
Use your solution for Hacky Sack to answer this question. Is the system meeting Hacky’s requirement of no waiting lines?
Select one:
a. Yes
b. No
Question 64
Question text
Hacky Sack wonders if it is worthwhile hiring an experienced and proficient ‘sales associate’ to work with Hacky. He estimates it will cost him a total of $18 per hour in wages and benefits for the associate – the same cost as for Hacky. From previous experience, he estimates the average waiting cost per client to be $0.35 per minute. What is the total hourly cost for the alternative of having two sales associates working at the store?
Select one:
a. $36.26
b. $51.75
c. $60.00
d. $18.70
Question 65
Question text
Hacky Sack wonders if it is worthwhile hiring one or two experienced and proficient ‘sales associates’ to service rental shop customers. He estimates it will cost him a total of $18 per hour in wages and benefits for each associate (the same cost as for himself). From previous experience, he estimates the average waiting cost per client to be $0.35 per minute. Which of the three scenarios provides the lowest total cost per hour for Hacky Sack’s shop?
Select one:
a. Just Hacky works in the store
b. Hacky hires one associate to work with him
c. Hacky hires two associates to work with hi
A schedule of activities is presented below
What is the expected time to complete the project using the regular times? Solve using Management Scientist. You do not need to crash the project.
Select one:
a. 19 days
b. 9 days
c. 28 days
d. 10 days
Question 67
Question text
Use the data given in the previous question to answer this question. What is the crash cost per day for Activity a?
Select one:
a. $10,000
b. $5,000
c. $2,000
d. $1,000
Question 68
Question text
Use the data given in question 66 to answer this question. What is the critical path?
Select one:
a. A-C-D
b. A-D-C
c. D-E-F
d. A-D-F
Question 69
Question text
The distance between different possible routes are shown in the table below.
How many arcs would you use in drawing the network diagram for this problem?
Path Distance
1 to 2 3
1 to 3 2
2 to 4 4
2 to 5 5
3 to 4 3
3 to 5 7
4 to 6 6
5 to 6 2
Select one:
a. 6
b. 7
c. 8
d. 2
Which of the following is not true regarding an LP model of the assignment problem?
Select one:
a. Costs appear in the objective function only.
b. All constraints are of the > form.
c. All constraint left-hand side coefficient values are 1.
d. All decision variable values are either 0 or 1.
Question 71
Question text
The assignment problem constraint X31 + X32 + X33 + X34 <= 2 means:
Select one:
a. agent 3 can be assigned to no more than 2 tasks
b. agent 2 can be assigned to 2 tasks
c. a mixture of agents 1, 2, 3, and 4 will be assigned to 2 tasks
d. agent 3 can be assigned to more than 2 tasks
Required Texts/Resources
Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J.D., & Martin, K. (2015). Quantitative Methods for Business (13th ed.), Cincinnati, OH: South-Western
