# DPURDUE Purdue West Lafayette 888Announcements Calendar Help vCRTUF 3"HS C3 | elMy CoursesOperationsFall 2022 MGMTKRANNERT_ONLINNDEPOT...

Name: __________________________________
Online MGMT 660 Final Exam, Fall2022
(Professors Suresh Chand)
INSTRUCTIONS:
1) Your submission is due by 10:00 pm Dec7th (Wednesday 10:00 pm EST).
2) You have 4 hours (in one sitting including breaks) to answer questions.
3) Open notes, laptop. Show your work.
4) Please do your own work. Communicating with others about the exam questions is not allowed. Cheating may result in a failing grade in the course.
5) If a question is not clear, please make necessary assumptions and make sure to write the assumptions you made.
6) Please type (or write) your answers and not cut-and-paste from any sources.
7) Please save a copy of your answer until the time when your grade has been posted. Once you receive your course grade, you should delete any copy of the exam or answer you may have saved. Thanks for your cooperation.
    Problem
    Your score
    Out of
    1
    
    15
    2
    
    10
    3
    
    15
    4
    
    15
    5
    
    19
    6
    
    26
    Total
    
    100

Good Luck!
Problem 1 [15 pts.]: Atlas Inc. is a toy bicycle manufacturing company producing a five-inch small version of the bike that Lance Armstrong rode to win his first Tour de France. The assembly of the bike requires completing seven tasks. Tasks need to be performed in the sequence 1 to 7. Task times are summarized here:
    Task
    Description
    Time (seconds)
    1
    The plastic tube for the frame is cut to size
    30 seconds
    2
    The tube is put together
    20 seconds
    3
    The frame is glued together
    35 seconds
    4
    The frame is cleaned
    25 seconds
    5
    Paint is sprayed onto the frame
    30 seconds
    6
    Wheels are assembled
    45 seconds
    7
    All other parts are assembled to the frame
    40 seconds
Under the current process layout, workers are allocated to the tasks as shown here:
· Worker 1: Tasks 1 and 2
· Worker 2: Task 3
· Worker 3: Tasks 4 and 5
· Worker 4: Task 6
· Worker 5: Task 7
Assume the workers are paid $15 per hour. Each bicycle is sold for $6 and includes parts that are sourced for $1. The company has fixed costs of $200 per hour. There exists substantially more demand for the bicycle than Atlas can supply.
a. What is the hourly capacity of the line with 5 workers and the current layout? [4 pts.]
The amount which has been paid to workers = $15/hr
The selling price of one bicycle along with parts = $6
The predefined fixed cost of the company = $200
Flow rate = 60*60/60 = 60
The number of workers = 5
Total wage per hour/flow rate = (6-1)*15/60= 75/60=0.75
The hourly capacity of the line with 5 workers is 0.75*5= 3.75
b. What is the average labor utilization of 5 workers if the line is producing 60 per hour? [4 pts.]
The labour time utilisation of 5 workers depends on the labour step and every time cost utilisation process in the case of 5 step process = 36
Labour cycle = 12*5 = 60
Therefore cycle step process = 60/36 = 60%
c. How much profit does the company make per hour if producing 60 per hour? [3 pts.]
The profit of the company in that case of producing 60 per hour is $240/hr as the company makes 4 times the amount of every worker.
d. The company is considering hiring one more worker, which will increase the number of workers from 5 to 6. By how much will the hourly capacity change by hiring one more worker? Show the optimal allocation of tasks to different workers. [4 pts.]
The hourly capacity will change from 3.75 to (0.75*6) = 4.5
The optimal allocation of tasks to the different workers varies from senior workers to junior workers. This is the reason the optimal allocation of tasks to different workers is 0.7% without the new worker.
Problem 2 (10 points): Alcoa is making long aluminum rods for the frame of airplanes for the Boeing Company. The current process produces these rods, which need to pass a tensile strength test. Alcoa collected 6 observations every two hours in the first shift. The X-bar’s and range are given below:
    Sample Number
    OBS. 1
    OBS. 2
    OBS. 3
    OBS. 4
    OBS. 5
    OBS. 6
    Mean
    Range
    1
    37.00
    37.50
    38.50
    40.00
    39.00
    42.00
    39.00
    5.00
    2
    38.00
    37.00
    41.50
    39.00
    38.50
    37.00
    38.50
    4.50
    3
    38.50
    42.50
    41.50
    42.00
    42.50
    42.00
    41.50
    4.00
    4
    37.00
    42.50
    41.00
    42.50
    42.00
    41.00
    41.00
    4.50
    
    
    
    
    
    
    
    
    
a.    Determine the control limits for the X-chart and the R-chart. [7 pts.]
The company Alcoa collected 6 observations every two hours.
a) The control limit of the X chart is 40.150
the quality control of the R chart is 4.338
b. The quality control manager tracked samples from the next four shifts and plotted the sample means and ranges in the X- chart and R-chart below. [3 pts.]
    
    
Using the control limits developed in (a), comment about the process.
The process includes bar diagram and data interpretation with the help of this chart and analysis the questions can be answered.
Problem 3 (15 points): Tom is in the business of selling a daily newspaper. The unit purchasing cost of a newspaper is $2.0. Tom sells the newspapers to the customers for a price of $4.0. If there are leftovers at the end of day, it can be sold to a recycling firm at $1.0 per paper. The probability distribution of demand for a given day is as follows:
    Demand
    300
    400
    500
    550
    600
    700
    800
    Probability
    0.25
    0.15
    0.15
    0.11
    0.14
    0.10
    0.10
a. What are Cu and Co? [2 pts.]
The cost of a newspaper is $2.0 the company sells to its customers for $4
C0 = demand/probability 300/0.25 = 1200
Cu = demand/probability 800/0.10 = 8000
b. If we increase order quantity from 500 to 501, by how much will the expected profit change? [3 pts.]
The increment order quantity is 500 to 501. The change in expected profit is 0.001 means 0.149.
c. What is the optimal order size which maximizes the expected profit? [5 pts.]
The optimal order size for the maximum profit is the last term of demand/probability.
d. Assuming Tom buys 400 copies of the newspaper. Calculate the expected profit. Use the table below for the calculations. [5 pts.]
If tom purchase 400 copies of the newspaper, the total amount tom may pay to the newspaper company is 400*2 = $800
The expected profit is $2 per newspaper for Tom who sells a copy of the newspaper for $4.
Q = 400
    Demand
    #Units sold
    #units leftover
    Revenue from #units sold
    Salvage from #units leftover
    Total cash inflow
    Probability
    300
    
    
    
    
    
    0.25
    400
    
    
    
    
    
    0.15
    500
    
    
    
    
    
    0.15
    550
    
    
    
    
    
    0.11
    600
    
    
    
    
    
    0.14
    700
    
    
    
    
    
    0.10
    800
    
    
    
    
    
    0.10
Problem 4 (15 points): The Stratosphere Corporation stocks part number MGT660, which it needs for the manufacturing of advanced communications satellites. Stratosphere's annual usage rate (i.e., its demand rate) for part MGT660 is constant and known to be 5000 units/year. ...