BA 380: Operations Management Homework

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WEEK 1 PROBLEM SOLVING ASSIGNMENT

DUE TUESDAY, JULY 22 (BEFORE THE CLASS)

Question 1

A company that makes shopping carts for supermarkets and other stores recently purchased

some new equipment that reduces the labor content of the jobs needed to product the shopping

carts. Prior to buying the new equipment, the company used five workers, who produced an

average of 80 carts per hour. Workers receive $10 per hour, and the machine cost was $40 per

hour. With the new equipment, it was possible to transfer one of the workers to another

department, and equipment cost increased by $10 per hour while output increased by four

carts per hour.

a. Compute labor productivity under each system. Use carts per worker per hour as the

measure of labor productivity.

b. Compute the multifactor productivity under each system. Use carts per dollar cost (labor

pus equipment) as the measure.

c. Comment on the changes in productivity according to the two measures, and on which one

you believe is the more pertinent for this situation.

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Question 2

The following table shows data on the average number of customers processed by several bank

service units each day. The hourly wage rate is $25, the overhead rate is 1.0 times labor cost,

and material cost is $5 per customer.

Unit Employees Customers Processed/Day

A 4 36 B 5 40 C 8 60 D 3 20

a. Compute the labor productivity and the multifactor productivity for each unit. Use an eight-

hour day for multifactor productivity.

b. Suppose a new, more standardized procedure is to be introduced that will enable each

employee to process one additional customer per day. Compute the expected labor and

multifactor productivity rates for each unit.

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Question 3

A company offers ID theft protection using leads obtained from client banks. Three employees

work 40 hours a week on the leads, at a pay rate of $25 per hour per employee. Each employee

identifies an average of 3,000 potential leads a week from a list of 5,000. An average of 4

percent actually sign up for the service, paying a one-time fee of $70. Material costs are $1,000

per week, and overhead costs are $9,000 per week. Calculate the multifactor productivity for

this operation in fees generated per dollar of input.

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Question 4

Lucky Lumen light bulbs have an expected life that is exponentially distributed with a mean of

20,000 hours. Determine the probability that one of these light bulbs will last.

a. At least 24,000 hours.

b. No longer than 4,000 hours.

c. Between 4,000 hours and 24,000 hours.

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Question 5

A machine can operate for an average of 10 weeks before it needs to be overhauled, a process

which takes two days. The machine is operated five days a week. Compute the availability of

this machine. (Hint: All times must be in the same units.)

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Question 6

A designer estimates that she can (a) increase the average time between failures of a part by 5

percent at a cost of $450, or (b) reduce the average repair time by 10 percent at a cost of $200.

Which option would be more cost-effective? Currently, the average time between failures is 100

hours and the average repair time is 4 hours.

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Question 7

A worker-machine operations was found to involve 3.3 minutes of machine time per cycle in the

course of 40 cycles of stopwatch study. The worker’s time averaged 1.9 minutes per cycle, and

the worker was given a rating of 120 percent (machine rating is 100 percent). Midway through

the study, the worker took a 10-minute rest break. Assuming an allowance factor of 12 percent

of work time, determine the standard time for this job.