Chapter 2, Problem 61P

To determine

(a)

The time required to build the 5^th house.

Answer to Problem 61P

The time required to the 5^th House is 2,833.65.

Explanation of Solution

Given information:

• Time required to produce 1^st unit = 3500 manual labor hours
• Learning curve = 92%

• Learning Curve: The learning curve captures the relationship between the task performance and task repetition

For estimating the time for repetitive tasks is given by following formula:

$\begin{array}{l}{{\displaystyle \text{T}}}_{\text{N}}\text{=}{{\displaystyle \text{T}}}_{\text{initial}}\text{×}{{\displaystyle \text{N}}}^{\text{b}}\\ \end{array}$

Where:

T_N− time required for Nth production

T_initial − time required for 1^st production

N − number of completed units

b − learning curve exponent

The learning curve exponent is calculated as

$\begin{array}{l}b=\frac{\log (LC)}{\log 2}\\ \end{array}$

Where: LC − Learning Curve.

Calculation:

We can now calculate the value of b (using the formula 2)

Using the formula (2):

$\begin{array}{l}b=\frac{\log (LC)}{\log 2}\\ b=\frac{\log (0.92)}{\log 2}\\ b=-0.1203\end{array}$

Using the formula (1):

• Calculating Time in Manual labor hours for constructing the 5^th house

$\begin{array}{l}{T}_N=T_{initial}\times N^b\\ T_5=3500\times 5^{-0.1203}\\ T_5=3500\times 0.8239\\ T_5=2,883.65\end{array}$.

Conclusion:

The time required to the 5^th House is 2,833.65.

To determine

(b)

The time required to build the 10^th house.

Answer to Problem 61P

The time required to build the 10^th house is 2,653.

Explanation of Solution

Given information:

• Time required to produce 1^st unit = 3500 manual labor hours
• Learning curve = 92%

• Learning Curve: The learning curve captures the relationship between the task performance and task repetition

For estimating the time for repetitive tasks is given by following formula:

$\begin{array}{l}{{\displaystyle \text{T}}}_{\text{N}}\text{=}{{\displaystyle \text{T}}}_{\text{initial}}\text{×}{{\displaystyle \text{N}}}^{\text{b}}\\ \end{array}$

Where:

T_N− time required for Nth production

T_initial − time required for 1^st production

N − number of completed units

b − learning curve exponent

The learning curve exponent is calculated as

$\begin{array}{l}b=\frac{\log (LC)}{\log 2}\\ \end{array}$

Where: LC − Learning Curve.

Calculation:

We can now calculate the value of b (using the formula 2)

Using the formula (2):

$\begin{array}{l}b=\frac{\log (LC)}{\log 2}\\ b=\frac{\log (0.92)}{\log 2}\\ b=-0.1203\end{array}$

Using the formula (1):

• Calculating Time in Person-hours for constructing the 10^th house

$\begin{array}{l}{T}_N=T_{initial}\times N^b\\ T_5=3500\times {10}^{-0.1203}\\ T_5=3500\times 0.7580\\ T_5=2,653\end{array}$.

Conclusion:

The time required to build the 10^th house is 2,653.

To determine

(c)

The time required to build the 18^th house.

Answer to Problem 61P

The time required to the construct the 18^th house is 2472.05.

Explanation of Solution

Given information:

• Time required to produce 1^st unit = 3500 manual labor hours
• Learning curve = 92%

• Learning Curve: The learning curve captures the relationship between the task performance and task repetition

For estimating the time for repetitive tasks is given by following formula:

$\begin{array}{l}{{\displaystyle \text{T}}}_{\text{N}}\text{=}{{\displaystyle \text{T}}}_{\text{initial}}\text{×}{{\displaystyle \text{N}}}^{\text{b}}\\ \end{array}$

Where:

T_N− time required for Nth production

T_initial − time required for 1^st production

N − number of completed units

b − learning curve exponent

The learning curve exponent is calculated as

$\begin{array}{l}b=\frac{\log (LC)}{\log 2}\\ \end{array}$

Where: LC − Learning Curve.

Calculation:

We can now calculate the value of b (using the formula 2)

Using the formula (2):

$\begin{array}{l}b=\frac{\log (LC)}{\log 2}\\ b=\frac{\log (0.92)}{\log 2}\\ b=-0.1203\end{array}$

Using the formula (1):

• Calculating Time in Person-hours for constructing the 18^th house

$\begin{array}{l}{T}_N=T_{initial}\times N^b\\ T_5=3500\times {18}^{-0.1203}\\ T_5=3500\times 0.7063\\ T_5=2,472.05\end{array}$.

Conclusion:

The time required to the construct the 18^th house is 2472.05.

To determine

(d)

The time required to build the 18^th house with 70% learning curve.

Answer to Problem 61P

The time required to the 18^th House with 70% learning curve is 790.65.

Explanation of Solution

Given information:

• Time required to produce 1^st unit = 3500 manual labor hours.
• Learning curve = 70%

• Learning Curve: The learning curve captures the relationship between the task performance and task repetition.

For estimating the time for repetitive tasks is given by following formula:

$\begin{array}{l}{{\displaystyle T}}_N={{\displaystyle T}}_{initial}\times {{\displaystyle N}}^b\\ \end{array}$

where:

T_N− time required for Nth production.

T_initial − time required for 1^st production.

N − number of completed units.

b − learning curve exponent.

The learning curve exponent is calculated as

$\begin{array}{l}b=\frac{\log (LC)}{\log 2}\\ \end{array}$

where: LC − Learning Curve.

Calculation:

• Learning Curve - 70%

We can now calculate the value of b (using the formula 2)

Using the formula (2):

$\begin{array}{l}b=\frac{\log (LC)}{\log 2}\\ b=\frac{\log (0.70)}{\log 2}\\ b=-0.5146\end{array}$

Using the formula (1):

• Calculating Time in Manual labor hours for constructing the 18^th house

$\begin{array}{l}{T}_N=T_{initial}\times N^b\\ T_5=3500\times {18}^{-0.5146}\\ T_5=3500\times 0.2259\\ T_5=790.65\end{array}$.

Conclusion:

The time required to the 18^th House with 70% learning curve is 790.65.

To determine

(e)

The time required to build the 18^th house with 75% learning curve.

Answer to Problem 61P

The time required to the 18^th House with 75% learning curve is1054.55.

Explanation of Solution

Given information:

• Time required to produce 1^st unit = 3500 manual labor hours
• Learning curve = 75%

• Learning Curve: The learning curve captures the relationship between the task performance and task repetition

For estimating the time for repetitive tasks is given by following formula:

$\begin{array}{l}{{\displaystyle T}}_N={{\displaystyle T}}_{initial}\times {{\displaystyle N}}^b\\ \end{array}$

where:

T_N− time required for Nth production

T_initial − time required for 1^st production

N − number of completed units

b − learning curve exponent

The learning curve exponent is calculated as

$\begin{array}{l}b=\frac{\log (LC)}{\log 2}\\ \end{array}$

where: LC − Learning Curve.

Calculation:

• Learning Curve - 75%

We can now calculate the value of b (using the formula 2)

Using the formula (2):

$\begin{array}{l}b=\frac{\log (LC)}{\log 2}\\ b=\frac{\log (0.75)}{\log 2}\\ b=-0.4150\end{array}$

Using the formula (1):

• Calculating Time in Manual labor hours for constructing the 18^th house

$\begin{array}{l}{T}_N=T_{initial}\times N^b\\ T_5=3500\times {18}^{-0.4150}\\ T_5=3500\times 0.3013\\ T_5=1054.55\end{array}$.

Conclusion:

The time required to the 18^th House with 75% learning curve is1054.55.

To determine

(f)

The time required to build the 18^th house with 80% learning curve.

Answer to Problem 61P

The time required to the 18^th House with 80% learning curve is 1380.05.

Explanation of Solution

Given information:

• Time required to produce 1^st unit = 3500 manual labor hours
• Learning curve = 80%

• Learning Curve: The learning curve captures the relationship between the task performance and task repetition

For estimating the time for repetitive tasks is given by following formula:

$\begin{array}{l}{{\displaystyle T}}_N={{\displaystyle T}}_{initial}\times {{\displaystyle N}}^b\\ \end{array}$

where:

T_N− time required for Nth production

T_initial − time required for 1^st production

N − number of completed units

b − learning curve exponent

The learning curve exponent is calculated as

$\begin{array}{l}b=\frac{\log (LC)}{\log 2}\\ \end{array}$

where: LC − Learning Curve.

Calculation:

• Learning Curve - 80%

We can now calculate the value of b (using the formula 2)

Using the formula (2):

$\begin{array}{l}b=\frac{\log (LC)}{\log 2}\\ b=\frac{\log (0.80)}{\log 2}\\ b=-0.3219\end{array}$

Using the formula (1):

• Calculating Time in Manual labor hours for constructing the 18^th house

$\begin{array}{l}{T}_N=T_{initial}\times N^b\\ T_5=3500\times {18}^{-0.3219}\\ T_5=3500\times 0.3943\\ T_5=1380.05\end{array}$.

Conclusion:

The time required to the 18^th House with 80% learning curve is 1380.05.