Question 1

The first unit of a product took 832 hours to build,and the learning curve is 90%.How long will it take to make the 25th unit? (Use at least three decimals in the exponent if you use the formula approach. )
A)time ≤ 500 hours
B)500 < time ≤ 525
C)525 < time ≤ 530
D)530 < time ≤ 550
E)time > 550

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Question 2

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.

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Question 3

Identify one advantage and one disadvantage of the doubling approach over the formula approach to learning curve calculations.

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Question 4

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.

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Question 5

The first unit of a product took 1,000 hours to build and the learning curve is 85%.How long will it take to make the first 5 units? (Use Table E.3)
A)less than 4,005 hours
B)from 4,005 to 4,015 hours
C)from 4,015 to 4,025 hours
D)from 4,025 to 4,035 hours
E)from 4,035 to 4,045 hours

Accepted Answer

Using Table E.3, we can find the cumulative average time for the first unit is 1,000 hours and the cumulative average time for the second unit is 850 hours (85% of 1,000 hours). Therefore, the total time for the first two units is 1,850 hours. For the third unit, we can find the cumulative average time by multiplying the time for the second unit by the learning curve factor of 85%, which gives us 723.5 hours (850 x 0.85). Adding this to the total time for the first two units, we get a total of 2,573.5 hours for the first three units. We can repeat this process for the fourth and fifth units:

Time for the fourth unit = 850 x 0.85^2 = 614.12 hours
Total time for the first four units = 1,000 + 850 + 723.5 + 614.12 = 3,187.62 hours

Time for the fifth unit = 850 x 0.85^3 = 522.00 hours 
Total time for the first five units = 1,000 + 850 + 723.5 + 614.12 + 522 = 4,009.62 hours

Therefore, the answer is from 4,025 to 4,035 hours, which is option D.

Question 6

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

Accepted Answer

We can use the following formula to find how long it will take to produce the 10th turbine:

Tn = a * n ^ log(1/L)

Where Tn is the time to produce the nth unit, a is the time to produce the first unit (7000 hours), n is the number of units produced (10 in this case), L is the learning rate (90%).

Plugging in the values, we get:

T10 = 7000 * (10 ^ log(1/0.9)) 
T10 = 7000 * (10 ^ -0.152) 
T10 = 7000 * 0.712 
T10 = 4984

So it will take approximately 4984 hours to produce the 10th turbine. Therefore, the best choice is C.

Question 7

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

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Question 8

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

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Question 9

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?

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Question 10

The first unit of a product took 50 hours to build,and the learning curve is 80%.How long will it take to make the third unit? (Use at least three decimals in the exponent if you use the formula approach. )
A)under 30 hours
B)about 32 hours
C)about 35 hours
D)about 50 hours
E)about 75 hours

Accepted Answer

Using the learning curve formula, we have:
$$T_n = T_1 	imes (n)^{\log(0.8)/\log(2)}$$
where $T_n$ is the time to build the nth unit, $T_1$ is the time to build the first unit (50 hours), the base of the logarithm is 2 because the learning rate is 80%, and the exponent is $\log(0.8)/\log(2) \approx -0.32193$.
Plugging in $n=3$, we get:
$$T_3 = 50 	imes (3)^{-0.32193} \approx 35.11$$
Therefore, the answer is choice C, about 35 hours.

Question 11

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

Accepted Answer

The labor time for the fourth unit can be calculated using the learning curve formula: T_n = T_1 * n^(log(b)/log(2)), where T_n is the time required to produce the nth unit, T_1 is the time required to produce the first unit, n is the unit number, and b is the learning rate (in decimal form). For the fourth unit (n=4) with an 80% learning curve (b=0.8), the formula becomes T_4 = 60 * 4^(log(0.8)/log(2)). This calculates to approximately 38.4 hours. At $10 per hour, the labor bill for the fourth unit is $384, which is $400 or less.

Question 12

To use the table of learning-curve coefficients,you must specify ________ and ________.

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Question 13

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

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Question 14

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?

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Question 15

The ________ is the simplest approach to learning curve problems.

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Question 16

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.

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Question 17

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?

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Question 18

The first unit of a product took 50 hours to build,and the learning curve is 85%.How long will it take to make the 10th unit? (Use at least three decimals in the exponent if you use the formula approach. )
A)less than 24 hours
B)from 25 to 30 hours
C)from 30 to 35 hours
D)from 35 to 40 hours
E)more than 40 hours

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Question 19

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

Accepted Answer

Using Table E.3, we can see that the cumulative average time for the fourth unit will be approximately 65 work days. 
To find the time for the first four units, we can use the formula:
Total Time = Time for First Unit x (1 + Learning rate)^-log(base 2) (Number of Units)
Total Time = 80 x (1 + 0.9)^-log(base 2)4
Total Time = 285.23 work days (rounded to the nearest whole number). 
Therefore, the time for the first four units will be about 285 work days.

Question 20

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.

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Quiz 26: Learning Curves

The first unit of a product took 832 hours to build,and the learning curve is 90%.How long will it take to make the 25th unit? (Use at least three decimals in the exponent if you use the formula approach. )

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.

Identify one advantage and one disadvantage of the doubling approach over the formula approach to learning curve calculations.

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.

The first unit of a product took 1,000 hours to build and the learning curve is 85%.How long will it take to make the first 5 units? (Use Table E.3)

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 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. )

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)

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?

The first unit of a product took 50 hours to build,and the learning curve is 80%.How long will it take to make the third unit? (Use at least three decimals in the exponent if you use the formula approach. )

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. )

To use the table of learning-curve coefficients,you must specify and .

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?

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?

The ________ is the simplest approach to learning curve problems.

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.

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?

The first unit of a product took 50 hours to build,and the learning curve is 85%.How long will it take to make the 10th unit? (Use at least three decimals in the exponent if you use the formula approach. )

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)

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.