Chapter 6, Problem 6OQ

a)

Summary Introduction

To determine: The estimate of the learning rate.

Introduction: It is the rate to measure the performance of the person in the new skills and in gaining experiences.

Explanation of Solution

Given information:

Estimate the learning rate for Unit 1 to Unit 2:

It is calculated by dividing the time taken to complete the second unit and first unit.

$\begin{array}{c}\text{Learning percentage}=\frac{\text{Time taken to complete second unit}}{\text{Time taken to complete first unit}}\\ =\frac{10}{12}\\ =83.33\%\end{array}$

Hence, the learning percentage is 83.33%.

Estimate the learning rate for Unit 2 to Unit 4:

It is calculated by dividing the time taken to complete the fourth unit and second unit.

$\begin{array}{c}\text{Learning percentage}=\frac{\text{Time taken to complete fourth unit}}{\text{Time taken to complete second unit}}\\ =\frac{6.5}{10}\\ =65\%\end{array}$

Hence, the learning percentage is 65%.

Estimate the learning rate for Unit 4 to Unit 8:

It is calculated by dividing the time taken to complete the eighth unit and fourth unit.

$\begin{array}{c}\text{Learning percentage}=\frac{\text{Time taken to complete eighth unit}}{\text{Time taken to complete fourth unit}}\\ =\frac{3.6}{6.5}\\ =55.38\%\end{array}$

Hence, the learning percentage is 55.38%.

Estimate the learning rate for Unit 8 to Unit 16:

It is calculated by dividing the time taken to complete the eighth unit and fourth unit.

$\begin{array}{c}\text{Learning percentage}=\frac{\text{Time taken to complete sixteenth unit}}{\text{Time taken to complete eighth unit}}\\ =\frac{2.7}{3.6}\\ =75\%\end{array}$

Hence, the learning percentage is 75%.

Determine the average learning rate:

$\begin{array}{c}\text{Average learning rate}=\frac{83.33\%+65\%+55.38\%+75\%}{4}\\ =\frac{278.71}{4}\\ =69.68\%\\ \simeq 70\%\end{array}$

Hence, the average learning rate is 70%.

b)

Summary Introduction

To determine: The bid that Company L should submit for the total order of 100 units.

Introduction: It is the rate to measure the performance of the person in the new skills and in gaining experiences.

Explanation of Solution

Given information:

Determine the average learning rate:

$\begin{array}{c}\text{Average learning rate}=\frac{83.33\%+65\%+55.38\%+75\%}{4}\\ =\frac{278.71}{4}\\ =69.68\%\\ \simeq 70\%\end{array}$

Hence, the average learning rate is 70%.

Determine the bid that Company L should submit for the total order of 100 units:

It is computed by subtracting the cumulative value for 20 units from cumulative value for 120 units and multiplying it with the cost to produce the first unit.

$\begin{array}{c}\begin{array}{l}\text{Cost to produce}\\ \text{100 more units}\end{array}\}=\left(\begin{array}{l}\text{Cumulative value for 120 units}-\\ \text{Cumulative value for 20 units}\end{array}\right)\times \left(\begin{array}{l}\text{Cost to produce}\\ \text{first unit}\end{array}\right)\\ =\left(19.570-7.407\right)\times \$12\text{ million}\\ =12.163\times \$12\text{ million}\\ =\$145,956,000\end{array}$

The cumulative values can be determined using the table of cumulative values. For example, 19.570 is the cumulative value for 120 units and 70% learning rate.

Hence, the bid that Company L should submit for the total order of 100 units is $145,956,000.

c)

Summary Introduction

To determine: The expected cost for the last unit under the learning rate.

Introduction: It is the rate to measure the performance of the person in the new skills and in gaining experiences.

Explanation of Solution

Given information:

Determine the average learning rate:

$\begin{array}{c}\text{Average learning rate}=\frac{83.33\%+65\%+55.38\%+75\%}{4}\\ =\frac{278.71}{4}\\ =69.68\%\\ \simeq 70\%\end{array}$

Hence, the average learning rate is 70%.

Determine the expected cost for the last unit under the learning rate:

It is computed by multiplying the cumulative value for 120 units with the cost to produce one unit.

$\begin{array}{c}\begin{array}{l}\text{Cost to produce}\\ {\text{120}}^{\text{th}}\text{ unit}\end{array}\}=\text{Cumulative value for 120 units}\times \left(\begin{array}{l}\text{Cost to produce}\\ \text{first unit}\end{array}\right)\\ =0.0851\times \$12\text{ million}\\ =\$1,021,200\end{array}$

The cumulative values can be determined using the table of cumulative values. For example, .0062 is the cumulative value for 120 units and 70% learning rate.

Hence, the expected cost to produce 120^th units is $1,021,200.