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24) The first unit of a product took 900 hours to build and the learning curve is 90%. How long will it take
to make the first 3 units? (Use Table E.3)
A) less than or equal to 2,470 hours
B) from 2,470 to 2,472 hours
C) from 2,472 to 2,475 hours
D) from 2,475 to 2,478 hours
E) from 2,478 to 2,481 hours
25) The first unit of a product took 80 work days. The learning curve is estimated to be 90%. The time for
the fourth unit will be about ________ work days and the time for the first four units will be about
________ work days. (Use Table E.3)
A) 51; 250
B) 250; 51
C) 65; 285
D) 51; cannot be determined
E) 65; cannot be determined
26) A defense contractor has just started producing turbines for a new government contract. The first
turbine took 7000 hours to produce. If the learning curve is 90%, how long will it take to produce the 10th
turbine? (Use at least three decimals in the exponent if you use the formula approach.)
A) less than 4800 hours
B) from 4800 to 4900 hours
C) from 4900 to 5000 hours
D) from 5000 to 5100 hours
E) over 5100 hours
27) A defense contractor has just started producing engines for a new government contract. The first
engine took 800 hours to produce. If the learning curve is 80%, how long will it take to produce the first
20 engines?
A) less than or equal to 1000 hours
B) from 1000 to 8000 hours
C) from 8000 to 8500 hours
D) from 8500 to 10000 hours
E) 10,000 or more hours
28) It took 60 hours to make the first unit of a product. After the second and third units were made, the
learning curve was estimated to be 80%. At $10 per hour, estimate the labor bill for the fourth unit. (Use
at least three decimals in the exponent if you use the formula approach.)
A) $400 or less
B) from $400 to $420
C) from $420 to $440
D) from $1800 to $2000
E) over $2000
29) A manager is trying to estimate the appropriate learning curve for a certain job. The manager notes
that the first four units had a total time of 30 minutes. Which learning curve would yield approximately
this result if the first unit took 9 minutes? (Use Table E.3.)
A) 0.70
B) 0.75
C) 0.80
D) 0.85
E) 0.90
30) The ________ is the simplest approach to learning curve problems.
31) To use the table of learning-curve coefficients, you must specify ________ and ________.
32) Identify one advantage and one disadvantage of the doubling approach over the formula approach to
learning curve calculations.
33) In the formula approach to learning curve calculations, you have used the formula TN = T1 (Nb). For a
problem with a 92 percent learning curve, what is b?
34) In the formula approach to learning curve calculations, you have used the formula TN = T1 (Nb). Your
manager shows you a problem for which b is specified as -.18443. What learning curve does that value
represent?
35) In the Learning-Curve Coefficients table for 70 percent learning, the sixth unit has a unit time value of
0.398. Verify that table entry by use of the formula approach. Use five decimals in your work.
36) The Learning-Curve Coefficients table reports that for 70 percent learning, the eighth unit has a unit
time value of 0.343. Verify that table entry by use of the doubling method.
37) Your firm has a contract to make 20 specialty lenses for night vision equipment. The first one took 40
hours. Learning is expected at the 85% learning curve. How long will it take to finish all 20 units?
38) Your firm has expertise with a special type of hand-finished furniture. The learning curve is known to
be 82%. If the first piece of furniture took 6 hours, use the formula approach to determine how long it will
take to make the third unit.
39) Your firm has expertise with a special type of hand-finished furniture. The learning curve is known to
be 82%. If the first piece of furniture took 6 hours, estimate (using the doubling approach) how long it will
take to complete the third unit.
40) The first unit took 79 hours; the tenth took 46 hours. What learning curve is implied by the data?
41) Your firm has expertise with a special type of hand-finished furniture. The learning curve is known to
be 82%. If the first piece of furniture took 6 hours, how long will it take to make the second? How long
will it take to make the fourth?
42) You are about to undertake the manufacture of a labor-intensive electronics component. The first unit
took 300 hours. You are not sure whether the learning curve is 70% or 80%. The initial phase of the
contract calls for 6 of these components.
a. How much time will it take to complete all six at 70% learning?
b. How much time will it take to complete all six at 80% learning?
43) A certain product under development took 200 hours for the production of its 2nd unit and 180 hours
for its 4th unit.
a. What is the learning curve?
b. How much time did the first unit take?
c. How much time would the production of the 10th unit take? (Use both the formula and the Table E.3
approach. Do the two versions agree?)
20
44) A contractor builds large ships for the Department of Defense. A recent contract called for 12
amphibious landing platforms. It was originally estimated that the first of these would cost $1 billion and
that 80 percent learning would be appropriate. In fact, the first ship cost $1.6 billion and the second $1.12
billion. What is the revised learning curve? What will be the total cost of the twelve ships? Is it higher or
lower than the original estimate? If the defense department cuts the contract from 12 ships to 9, what
happens to the average cost per ship?
45) A small manufacturer that offers "hand crafted" furniture has developed a new style of desk that they
believe will be very successful in the marketplace. It is expected that the first desk will take about 60
hours of craftsmen's time to complete. They expect a 90% learning curve for this desk.
How long will it take to make the 20th desk? The firm is considering accepting an order for 25 desks.
How many hours of labor will this require for all 25?
46) Your company is making experimental turbochargers for a new design of high-powered farm tractors.
The production schedule for these new components is contained in the table below.
Month
Turbochargers
1
4
2
6
3
7
4
8
5
5
The first turbocharger, a trial unit, took 900 hours to produce. Based on your experience with similar
products, the learning curve is 85%. You have 20 employees, and each employee works 160 hours per
month. How many hours will be required in each month? In which month(s) will overtime be required to
meet the production schedule?
47) Sally suspects strongly that there is a learning curve associated with solving problems assigned for
operations management. She notes that it took her approximately 33 minutes to solve the first problem
and 20 minutes to solve the fifth problem.
a. Estimate Sally's learning curve.
b. Using your answer from part a, estimate how much longer it will take Sally to finish the three
problems that remain.
48) Joe's Manufacturing is considering bidding on a small order for 5 units. Based on similar products
that they have made in the past, they believe that the first unit will take 500 labor hours. They also believe
that there will be an 80% learning curve. How many hours of labor should Joe include for his bid?
49) A company is preparing a bid on a government contract for 40 units of a certain product. The
operations manager estimates the assembly time required for the first two units to be 10.4 hours and 8.3
hours, respectively.
a. What is the appropriate learning curve?
b. What is the average time per unit for the 40 units?
c. Which unit, if any, will require approximately one-half the time of the first unit?
50) A small manufacturer builds wooden pleasure boats in a craftsman manner by traditional labor-
intensive methods. The first boat is estimated to take 650 hours of skilled labor, which cost $40 per hour.
They currently have three workers that can work 2,000 hours a year. They assume that there is a 90%
learning curve. How many boats can they build in their first year?
51) You are a cost accountant for a firm that specializes in "small" (under 10 billion dollars) defense
contracts for specialty electronics products, such as fully portable, miniaturized CD-ROM imaging
stations and global positioning transmitters/transponders. Your company is well respected in this field.
One project up for competitive bids is a Field Service, Hands-Free, Individual Multi-Protocol Secure
Communicator (a battlefield version of a cellular telephone, but built into each soldier's helmet, and
containing necessary encryption technology). The Department of Defense wants 8 of these experimental
devices to test their practicality. You have reviewed the contract specifications, and estimated that the
first FSHFIMPSC should require 2350 hours, and that the product is subject to a 75% learning curve. All
costs of the project (machine purchase, machine time, direct and indirect labor, and materials) have been
bundled (allocated) into an hourly labor rate of $172 per hour. Determine the total project cost using the
provided data.
52) A metal works fabricator is about to release a new model of his firm's copper sculpture and fountain.
The operations manager estimates that this product is subject to a 90 percent learning curve on labor
only–the material bill is not affected by experience. The firm prices its work based on cost–the sum of
materials plus 30 percent and labor plus 50 percent. (This allows the firm to practice a form of "demand
management" for its very popular works.) The first item has already been finished; the material bill was
$800 and labor totaled 40 hours. The firm pays its metalworking artisans an average of $18 per hour.
What should be the asking price of the first unit? The second?
53) Using the doubling approach, determine how long it will take to make the 64th unit of a product if it
took 1 hour to complete the first product with a 50% learning curve.
54) A product was priced assuming an 80% learning curve. How much extra labor (in %) will be required
on the 4th product if the learning curve is actually 90%?
55) A product was priced assuming an 80% learning curve. How much extra labor (in $) will be required
on the 4th product if the learning curve is actually 90%? Assume that the first unit cost $100 to produce.
56) The fourth unit of production took 80 minutes while the ninth unit of production took 50 minutes.
How long did the first unit take?
57) The seventh unit of production took 63.423 minutes while the ninth unit of production took 59.8
minutes. What is the improvement rate?
Section 4 Strategic Implications of Learning Curves
1) A firm that successfully pursues a steeper-than-industry-average learning curve and manages costs
down may still fail if, by underestimating a strong competitor, it fails to gain the added volume necessary
for the learning curve to exist.
2) On an ordinary graph, unit times for a learning curve decrease at a decreasing rate, but on a log-log
graph, the learning "curve" appears as a straight line.
3) Which one of the following courses of actions would NOT be taken by a firm wanting to pursue a
learning curve steeper than the industry average?
A) following an aggressive pricing policy
B) focusing on continuing cost reduction
C) keeping capacity equal to demand to control costs
D) focusing on productivity improvement
E) building on shared experience
4) Companies pursuing a learning curve strategy MUST increase which of the following?
A) employee training
B) costs
C) quality
D) volume
E) all of the above
5) Which of the following is representative of a firm pursuing a learning-curve strategy?
A) aggressive pricing policy
B) focus on productivity improvement
C) building on shared experience
D) keeping capacity growing ahead of demand
E) all of the above
6) When learning curves are plotted on ________ scales, the "curves" become straight lines.
Section 5 Limitations of Learning Curves
1) Reevaluation of learning curves is inappropriate.
2) Which of the following is FALSE regarding learning curves?
A) Learning curves differ from company to company.
B) The same learning curves are used for indirect labor as are used for direct labor.
C) Changes in personnel can change the learning curve.
D) The learning curve may spike for a short time even if it is going to drop in the long run.
E) All of the above are false.
3) Which of the following is a limitation of the use of learning curves?
A) Change in personnel, design, or procedure leave the learning curve unchanged.
B) Learning curves are applicable to services as well as to manufacturing.
C) The culture of the workplace may alter the learning curve.
D) Direct labor and indirect labor follow the same learning curves.
E) Applications of learning curves are of tactical, not strategic, importance.
4) Which of the following is NOT a limitation of the use of learning curves?
A) Any change in personnel, design, or procedure can alter the learning curve.
B) Time measurements on early units completed must be accurate.
C) The culture of the workplace may alter the learning curve.
D) Direct labor and indirect labor may not follow the same learning curves.
E) All of these are limitations of learning curves.
5) What cautions are in order when using learning curves?
6) What can cause a learning curve to vary from a smooth downward slope?
