Chapter 6, Problem 8OQ

a)

Summary Introduction

To determine: The time and parts costs for the dozen 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:

The first unit produced by Company L took 5,000 hours for production and required $250,000 worth of material. The second unit took 3,500 hours and $200,000. It is given that labor is $30 per hour.

Estimate the learning rate for labor:

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.

$\begin{array}{c}\text{Learning percentage}=\frac{\text{Time taken to complete second unit}}{\text{Time taken to complete first unit}}\\ =\frac{3,500}{5,000}\\ =70\%\end{array}$

Hence, the learning percentage is 70%.

Estimate the learning rate for material:

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.

$\begin{array}{c}\text{Learning percentage}=\frac{\text{Time taken to complete second unit}}{\text{Time taken to complete first unit}}\\ =\frac{200,000}{250,000}\\ =80\%\end{array}$

Hence, the learning percentage is 80%.

Determine the labor cost for 10 more units:

It is computed by subtracting the cumulative value for 2 units from cumulative value for 12 units and multiplying it with the time to produce first unit and labor cost per hour.

$\begin{array}{c}\begin{array}{l}\text{Labor cost for}\\ \text{10 more units}\end{array}\}=\left(\begin{array}{l}\text{Cumulative value for 12 units}-\\ \text{Cumulative value for 2 units}\end{array}\right)\times \left(\begin{array}{l}\text{Time to produce}\\ \text{first unit}\end{array}\right)\times \left(\begin{array}{l}\text{Labor cost}\\ \text{per hour}\end{array}\right)\\ =\left(5.501-1.700\right)\times 5,000\times 30\\ =3.801\times 5,000\times 30\\ =\$570,150\end{array}$

The cumulative values can be determined using the table of cumulative values. For example, 5.501 is the cumulative value for 12 units and 70% learning rate.

Hence, the labor cost for 10 more units is $570,150.

Determine the material cost for 10 more units:

It is computed by subtracting the cumulative value for 2 units from cumulative value for 12 units and multiplying it with the time to produce first unit and labor cost per hour.

$\begin{array}{c}\begin{array}{l}\text{Material cost for}\\ \text{10 more units}\end{array}\}=\left(\begin{array}{l}\text{Cumulative value for 12 units}-\\ \text{Cumulative value for 2 units}\end{array}\right)\times \left(\begin{array}{l}\text{Cost to produce}\\ \text{first unit}\end{array}\right)\\ =\left(7.227-1.800\right)\times 250,000\\ =5.427\times 250,000\\ =\$1,356,750\end{array}$

The cumulative values can be determined using the table of cumulative values. For example, 5.427 is the cumulative value for 12 units and 80% learning rate.

Hence, the material cost for 10 more units is $1,356,750.

Compute the total cost:

It is computed by adding labor cost and material cost.

$\begin{array}{c}\text{Total cost}=\text{Labor cost}-\text{Material cost}\\ =\$570,150+\$1,356,750\\ =\$1,926,900\end{array}$

Hence, the total cost is $1,926,900.

b)

Summary Introduction

To determine: The way the reassignment of personnel and equipment to another project would affect the subsequent bid.

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:

The first unit produced by Company L took 5,000 hours for production and required $250,000 worth of material. The second unit took 3,500 hours and $200,000. It is given that labor is $30 per hour.

Determine the labor cost for 10 more units:

$\begin{array}{c}\begin{array}{l}\text{Labor cost for}\\ \text{10 more units}\end{array}\}=\left(\begin{array}{l}\text{Cumulative value}\\ \text{for 10 units}\end{array}\right)\times \left(\begin{array}{l}\text{Time to produce}\\ \text{first unit}\end{array}\right)\times \left(\begin{array}{l}\text{Labor cost}\\ \text{per hour}\end{array}\right)\\ =\left(4.931\right)\times 5,000\times 30\\ =\$739,650\end{array}$

The cumulative values can be determined using the table of cumulative values. For example, 4.931 is the cumulative value for 10 units and 70% learning rate.

Hence, the labor cost for 10 more units is $739,650.

Determine the material cost for 10 more units:

$\begin{array}{c}\begin{array}{l}\text{Material cost for}\\ \text{10 more units}\end{array}\}=\left(\begin{array}{l}\text{Cumulative value}\\ \text{for 10 units}\end{array}\right)\times \left(\begin{array}{l}\text{Cost to produce}\\ \text{first unit}\end{array}\right)\\ =6.315\times \$250,000\\ =\$1,578,750\end{array}$

The cumulative values can be determined using the table of cumulative values. For example, 6.315 is the cumulative value for 10 units and 80% learning rate.

Hence, the material cost for 10 more units is $1,578,750.

Compute the total cost:

It is computed by adding labor cost and material cost.

$\begin{array}{c}\text{Total cost}=\text{Labor cost}-\text{Material cost}\\ =\$739,650+\$1,578,750\\ =\$2,318,400\end{array}$

Hence, the total cost is $2,318,400.