Use the following to answer questions 1-5: A company is designing a product layo
ID: 360477 • Letter: U
Question
Use the following to answer questions 1-5:
A company is designing a product layout for a new product. It plans to use this production line eight hours a day in order to meet projected demand of 480 units per day. The tasks necessary to produce this product:
1. Without regard to demand, what is the minimum possible cycle time (in seconds) for this situation?
A. 162
B. 72
C. 54
D. 12
E. 60
2. If the company desires that output rate equal demand, what is the desired cycle time (in seconds)?
A. 162
B. 72
C. 54
D. 12
E. 60
3. If the company desires that output rate equal demand, what is the minimum number of workstations needed?
A. 3
B. 4
C. 5
D. 6
E. 7
4. If the company desires that output rate equal demand, what would be the efficiency of this line with the minimum number of workstations?
A. 100%
B. 92.5%
C. 75%
D. 87.5%
E. 90%
5. If the company desires that output rate equal demand, what is the last task performed at the second workstation in the balance which uses the minimum number of workstations?
A. u
B. v
C. w
D. x
E. y
Use the following to answer questions 6-10:
The production planner for Fine Coffees, Inc. produces two coffee blends: American (A) and British (B). Two of his resources are constrained: Columbia beans, of which he can get at most 300 pounds (4,800 ounces) per week; and Dominican beans, of which he can get at most 200 pounds (3,200 ounces) per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound.
6. What is the objective function?
A. $1 A + $2 B = Z
B. $12 A + $8 B = Z
C. $2 A + $1B = Z
D. $8 A + $12 B = Z
E. $4 A + $8 B = Z
7. What is the Columbia bean constraint?
A. 1 A + 2 B 4,800
B. 12 A + 8 B 4,800
C. 2 A + 1 B 4,800
D. 8 A + 12 B 4,800
E. 4 A + 8 B 4,800
8. Which of the following is not a feasible production combination?
A. 0 A & 0 B
B. 0 A & 400 B
C. 200 A & 300 B
D. 400 A & 0 B
E. 400 A & 400 B
9. What are optimal weekly profits?
A. $0
B. $400
C. $700
D. $800
E. $900
10. For the production combination of 0 American and 400 British, which resource is "slack" (not fully used)?
A. Colombian beans (only)
B. Dominican beans (only)
C. both Colombian beans and Dominican beans
D. neither Colombian beans nor Dominican beans
E. cannot be determined exactly
Use the following to answer Questions 11-12
A design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company produces. He knows from numerous previous samples that this service life is normally distributed with a mean of 500 hours and a standard deviation of 20 hours. On three recent production batches, he tested service life on random samples of four headlamps, with these results:
11. What is the mean of the sampling distribution of sample means when service life is in control?
A. 250 hours
B. 470 hours
C. 495 hours
D. 500 hours
E. 515 hours
12. If he uses upper and lower control limits of 520 and 480 hours, on what sample(s) (if any) does service life appear to be out of control?
A. sample 1
B. sample 2
C. sample 3
D. both samples 2 and 3
E. all samples are in control
Use the following to answer Questions 13-14
The Chair of the Operations Management Department at Quality University wants to construct a p-chart for determining whether the four faculties teaching the basic P/OM course are under control with regard to the number of students who fail the course. Accordingly, he sampled 100 final grades from last year for each instructor, with the following results: 13. What are the .95 (5% risk of Type I error) upper and lower control limits for the p-chart?
A. .95 and .05
B. .13 and .07
C. .1588 and .0412
D. .16 and .04
E. .1774 and .0226 14.
Using .95 control limits, (5% risk of Type I error), which instructor(s), if any, should he conclude is (are) out of control? A. none
B. Prof. B
C. Prof. D
D. both Prof. B and Prof. D
E. all
15. The specifications for a product are 6 mm 0.1 mm. The process is known to operate at a mean of 6.05 with a standard deviation of 0.01 mm. What is the Cpk for this process?
A. 3.33
B. 1.67
C. 5.00
D. 2.50
E. none of the above
Use the following to answer Questions 16-20
The manager of the Quick Stop Corner Convenience Store (which never closes) sells four cases of Stein beer each day. Order costs are $8.00 per order, and Stein beer costs $.80 per six-pack (each case of Stein beer contains four six-packs). Orders arrive three days from the time they are placed. Daily holding costs are equal to five percent of the cost of the beer.
16. At what point should he reorder Stein beer?
A. 0 cases remaining
B. 4 cases remaining
C. 12 cases remaining
D. 16 cases remaining
E. 20 cases remaining
17. If he were to order 16 cases of Stein beer at a time, what would be the length of an order cycle?
A. 0.25 days
B. 3 days
C. 1 day
D. 4 days
E. 20 days
18. If he were to order 16 cases of Stein beer at a time, what would be the average inventory level?
A. 4 cases
B. 12 cases
C. 8 cases
D. 20 cases
E. 16 cases 1
9. If he were to order 16 cases of Stein beer at a time, what would be the daily total inventory costs, EXCLUDING the cost of the beer?
A. $2.00
B. $4.00
C. $1.28
D. $3.28
E. $2.56
20. What is the economic order quantity for Stein beer?
A. 8 cases
B. 11 cases
C. 14 cases
D. 20 cases
E. 32 cases
Task Time (sec) Immmediate Predcessor u 30 none v 30 u w 6 u x 12 w y 54 x z 30 v,yExplanation / Answer
Answer question 1 :
The Predecessor diagram of tasks as follows :
U
V
W
X
Y
Z
The possible parallel paths and their corresponding durations as follows :
U-V-Z = 30 + 30 + 30 = 90 seconds
U-W-X-Y-Z = 30 + 6 + 12 + 54 + 30 =132 Since , U-W-X-Y-Z has the longer duration, it forms the critical path with product throughput time of 132 seconds.
Since , Y in the critical path has the longest duration of 54 seconds, it forms the bottleneck task and minimum cycle time will be determined by time required for activity Y.
Therefore Minimum Cycle time = 54 seconds
MINIMUM POSSIBLE CYCLE TIME = 54 SECONDS
Answer to question 2 :
Required demand is 480 units in a day of 8 hours i.e. 480 minutes
Therefore , Cycle time = 480 minutes/ 480 units = 1 minute/ unit ( 60 seconds/ unit )
DESIRED CYCLE TIME = 60 SECONDS
Answer to question 3 :
Total duration of all tasks ( U to Z ) = 30 + 30 + 6 + 12 + 54 + 30 seconds = 162 seconds
Therefore , minimum number of workstations needed
= Total duration of all tasks / Required cycle time
= 162/ 60
= 2.7 ( 3 rounded to nearest whole number )
NUMBER OF WORKSTATIONS REQUIRED = 3
Answer to question 4 :
Arrangement of workstations :
Workstation
Activities
Duration ( seconds )
1
U, W,X
30 + 6 + 12 = 48
2
V, Z
60
3
Y
54
Efficiency of the line with the minimum number of workstations
= Total duration of all tasks / ( Number of workstations x Cycle time ) x 100
= 162/ ( 3 x 60 ) x 100
= 90%
EFFICIENCY OF THIS LINE = 90 %
Answer to question 5 :
Last task performed in second workstation in balance is “Z”
U
V
W
X
Y
Z
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