Question 1

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

Accepted Answer

The answer of The first unit of a product took...

Question 2

The first unit of production took 10 hours with an 80% learning curve. How long will it take to complete both the first and second units?
A) 10 hours
B) 8 hours
C) 18 hours
D) none of the above
E) There is not enough information to solve the problem.

Accepted Answer

With an 80% learning curve, the time required to complete the first unit is 10 hours. For the second unit, we use the learning curve formula: Time for second unit = Time for first unit x (learning curve percentage/100) ^ log2(2) = 10 x (80/100) ^ 1 = 8 hours. Therefore, the total time to complete both units is 10 + 8 = 18 hours. Hence, the answer is option C.

Question 3

The first unit took 10 hours and the eighth unit took 1.25 hours. What is the learning curve?
A) 50%
B) 90%
C) 80%
D) 12.5%
E) none of the above

Accepted Answer

The answer of The first unit took 10 hours and...

Question 4

The first unit took 10 hours and the fourth unit 8.1 hours. What is the improvement rate?
A) 99%
B) 95%
C) 90%
D) 15%
E) none of the above

Accepted Answer

The improvement rate can be calculated using the formula for learning curve or improvement rate: $IR = \left(\frac{T_n}{T_1}\right)^{\frac{1}{n-1}}$, where $T_n$ is the time taken for the nth unit, $T_1$ is the time taken for the first unit, and $n$ is the unit number. For the fourth unit ($n=4$), $T_1=10$ hours and $T_4=8.1$ hours, the formula becomes $IR = \left(\frac{8.1}{10}\right)^{\frac{1}{4-1}}$, which simplifies to $IR = \left(0.81\right)^{\frac{1}{3}}$. This does not match any of the provided options exactly, indicating the correct answer is E, none of the above.

Question 5

It took 18 hours to complete the first two products with an 80% learning curve. How long did the second product take?
A) 8 hours
B) 10 hours
C) 18 hours
D) 8.1 hours
E) none of the above

Accepted Answer

With an 80% learning curve, the time to produce the second product is 80% of the time it took to produce the first. If the first two products took 18 hours together, and assuming the first product took X hours, then the second took 0.8X hours. The equation is X + 0.8X = 18, solving for X gives X = 10 for the first product, so the second product took 0.8 * 10 = 8 hours.

Question 6

The first unit took 10 hours and the third unit took 5.7 hours. What is the improvement rate?
A) 70%
B) 30%
C) 50%
D) 90%
E) 10%

Accepted Answer

To calculate the improvement rate, we need to compare the time taken by the first unit with the time taken by the third unit.

Improvement rate = ((time taken by first unit - time taken by third unit) / time taken by first unit) x 100%

Improvement rate = ((10 - 5.7) / 10) x 100%
Improvement rate = (4.3 / 10) x 100%
Improvement rate = 0.43 x 10
Improvement rate = 4.3

Therefore, the improvement rate is 43%, which is closest to option B) 30%.

Question 7

The first product took 10 hours to build and the learning curve is estimated to be 90%. How long with it take to make the fourth unit?
A) 10 hours
B) 9 hours
C) 8.1 hours
D) 7.5 hours
E) none of the above

Accepted Answer

With a learning curve of 90%, we can use the following formula to estimate the time it takes to build subsequent units: 
T2 = T1 * (0.9)^log2(N2/N1) 
Where T1 is the time it takes to build the first unit, N1 is the quantity of the first unit, N2 is the quantity of the subsequent unit we want to build, and T2 is the estimated time it will take to build the subsequent unit.

For the fourth unit, N2 is 4 because we want to build four units in total. Therefore: 
T2 = 10 * (0.9)^log2(4/1) 
T2 = 8.1

Therefore, the answer is choice C) 8.1 hours.

Question 8

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 logarithmic 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: Tn = T1 * n^(log b / log 2), where Tn is the time required for the nth unit, T1 is the time required for the first unit, n is the unit number, and b is the learning rate (in this case, 80% or 0.8). For the fourth unit, the formula becomes T4 = 60 * 4^(log 0.8 / log 2). Calculating the exponent: log 0.8 / log 2 ≈ -0.322 (using at least three decimals as instructed). Thus, T4 ≈ 60 * 4^(-0.322) ≈ 60 * 0.6 ≈ 36 hours. At $10 per hour, the labor bill for the fourth unit is 36 * $10 = $360, which is $400 or less.

Question 9

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

To find the time for the fourth unit, we can use the formula for the learning curve:

Time for nth unit = Time for first unit * n^log(0.9)/log(2)

Plugging in n=4, we get:

Time for fourth unit = 80 * 4^log(0.9)/log(2) 
                     = 65.4 work days (rounded to nearest integer)

To find the time for the first four units, we can use Table E.3 to find the cumulative average time for four units at a learning rate of 90%. Reading from the table, we find that the cumulative average time for four units is 1.61 times the time for one unit. Therefore:

Time for first four units = 80 * 1.61 
                         = 128.8 work days (rounded to nearest integer)

Since 65.4 and 128.8 are closest to the values in choice C, the answer is C.

Question 10

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? (Use at least three decimals in the exponent if you use the logarithmic approach, or use Table E.3 cumulative coefficient)
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

Accepted Answer

We can use the learning curve formula to find the time it takes to produce a certain number of engines:
T₂ = T₁ * (N₂/N₁)^log(0.8)

where T₁ is the time it takes to produce the first engine, N₁ is the quantity of engines produced when T₁ is reached, N₂ is the desired quantity of engines, and log(0.8) is the learning curve coefficient.

For the first 20 engines,
T₂ = 800 * (20/1)^log(0.8)
T₂ = 8552.049 hours

Therefore, the answer is choice C, from 8000 to 8500 hours.

Question 11

The second unit of production took 9 hours. If the learning curve is 90% how long did the first unit take?
A) 9 hours
B) 10 hours
C) 8.1 hours
D) 8.5 hours
E) none of the above

Accepted Answer

The answer of The second unit of production took 9...

Question 12

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 cumulative coefficient)
A) 0.70
B) 0.75
C) 0.80
D) 0.85
E) 0.90

Accepted Answer

The answer of A manager is trying to estimate the...

Question 13

The first unit took 10 hours and the fourth unit took 8.1 hours to complete. What is the learning curve?
A) 100%
B) 99%
C) 95%
D) 90%
E) 80%

Accepted Answer

The learning curve is 90%. This is determined by using the formula for calculating the learning rate when the time to produce the first and the nth units are known. The formula involves taking the nth root (in this case, the 4th root since we're looking at the fourth unit) of the ratio of the time it takes to produce the nth unit over the time it takes to produce the first unit, then multiplying by 100 to get a percentage. In this case, (8.1 / 10)^(1/3) * 100 ≈ 90%, indicating a 90% learning curve, which means each time the production doubles, the time taken to produce each unit reduces to 90% of the previous time.

Question 14

A company negotiates a price for two aircraft that includes a reduction in labor on the second aircraft consistent with a 70% learning curve. Suppose the first aircraft took 100 hours. If the improvement rate changes to 20%, how will the total time to complete both aircraft change?
A) no change
B) -10 hours
C) + 10 hours
D) -50 hours
E) + 50 hours

Accepted Answer

From the information given, we know that the second aircraft will take:
100 * 0.7 ^ log2(2) = 70 hours

However, if the improvement rate changes to 20%, the new learning curve coefficient is:
b' = b / (1 - 0.2 * b) = 0.7 / (1 - 0.2 * 0.7) = 0.8246

Using this new coefficient, the second aircraft will take:
100 * 0.8246 ^ log2(2) = 82.46 hours

So the total time to complete both aircraft is:
100 + 70 + 82.46 = 252.46 hours

Compared to the original total time:
100 + 70 = 170 hours

The change in total time is:
252.46 - 170 = 82.46 hours

This is an increase of:
82.46 - 70 = 12.46 hours

Rounding to the nearest 10, we get:
+10 hours, which is answer choice C.

Question 15

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 logarithmic 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

Accepted Answer

The time to produce the nth unit in a learning curve is given by T_n = T_1 * n^b, where T_1 is the time to produce the first unit, n is the unit number, and b is the learning curve index, calculated as b = log(learning percentage) / log(2). For an 85% learning curve, b = log(0.85) / log(2) ≈ -0.234. Thus, the time for the 10th unit, T_10 = 50 * 10^(-0.234) ≈ 28.398 hours, which falls in the range from 25 to 30 hours.

Question 16

Suppose that there are two products with the same first product time. However, product A has an improvement rate of 10% while product B has an improvement rate of 20%. How much longer will it take to make the 10^th unit of product A compared to product B? A) Both will have the identical time for the 10^th unit. B) A will take 48% more time. C) A will take 48% less time. D) A will take 23% less time. E) none of the above

Accepted Answer

Let's assume both products take x time to make the 10^th unit. For product A, the improved time can be calculated as: Improved time = x - (10% of x) = 0.9x For product B, the improved time can be calculated as: Improved time = x - (20% of x) = 0.8x We need to find how much longer product A will take compared to product B. Time difference = Improved time for product A - Improved time for product B Time difference = 0.9x - 0.8x Time difference = 0.1x Therefore, product A will take 10% longer time than product B. Time difference as a percentage of the improved time for product B can be calculated as: (Time difference / Improved time for product B) x 100 = (0.1x / 0.8x) x 100 = 12.5% So, product A will take 12.5% longer time than product B. If we consider the time it takes to make the product initially, A will take 48% more time than B.

Question 17

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 logarithmic 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 learning curve formula: 𝑇𝑛 = 𝑎𝑇1/𝑏
where 𝑇𝑛 is the time for producing the nth turbine,
𝑇1 is the time for producing the first turbine (7000 hours),
a is an arbitrary constant,
and b is the learning percentage (90% = 0.90).

To find a, we can use the given information on the first turbine:
7000 = a(1)^b
7000 = a
Thus, a = 7000.

Now we can find the time for producing the 10th turbine:
𝑇10 = 7000(10)^log(0.90)/log(2)
𝑇10 ≈ 4935.84 hours

Therefore, the best choice is C, from 4900 to 5000 hours.

Question 18

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 logarithmic approach.)
A) time ≤ 500 hours
B) 500 < time ≤ 525
C) 525 < time ≤ 530
D) 530 < time ≤ 550
E) time > 550

Accepted Answer

The learning curve formula is Tn = T1 * n^(log b / log 2), where Tn is the time it takes to produce the nth unit, T1 is the time it takes to produce the first unit, n is the unit number, and b is the learning rate (in decimal form). For a 90% learning curve, b = 0.9. Plugging in the values: T25 = 832 * 25^(log 0.9 / log 2) ≈ 520.8 hours. This falls into the range of 500 < time ≤ 525.

Question 19

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

The answer of The first unit of a product took...

Question 20

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 logarithmic 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:
$Time\ to\ make\ n\ units = T_1 * n^{\log_2(0.8)}$
For the third unit, we have:
$T_3 = T_1 * 3^{\log_2(0.8)}$
Plugging in the values, we get:
$T_3 = 50 * 3^{\log_2(0.8)} \approx 34.99$
Therefore, the answer is approximately 35 hours. Choice C is the closest option.

Quiz 22: Vehicle Routing and Scheduling

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)

The first unit of production took 10 hours with an 80% learning curve. How long will it take to complete both the first and second units?

The first unit took 10 hours and the eighth unit took 1.25 hours. What is the learning curve?

The first unit took 10 hours and the fourth unit 8.1 hours. What is the improvement rate?

It took 18 hours to complete the first two products with an 80% learning curve. How long did the second product take?

The first unit took 10 hours and the third unit took 5.7 hours. What is the improvement rate?

The first product took 10 hours to build and the learning curve is estimated to be 90%. How long with it take to make the fourth unit?

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 logarithmic 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 second unit of production took 9 hours. If the learning curve is 90% how long did the first unit take?

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 cumulative coefficient)

The first unit took 10 hours and the fourth unit took 8.1 hours to complete. What is the learning curve?

A company negotiates a price for two aircraft that includes a reduction in labor on the second aircraft consistent with a 70% learning curve. Suppose the first aircraft took 100 hours. If the improvement rate changes to 20%, how will the total time to complete both aircraft change?

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 logarithmic approach.)

Suppose that there are two products with the same first product time. However, product A has an improvement rate of 10% while product B has an improvement rate of 20%. How much longer will it take to make the 10^th unit of product A compared to product B?

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 logarithmic approach.)

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 logarithmic approach.)

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)

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 logarithmic approach.)