Chapter 6, Problem 10OQ

a)

Summary Introduction

To determine: The last unit cost to build.

Explanation of Solution

Given information:

It is given that first unit took 4,000 hours to complete and the cost for materials and equipment usage is $30,000. Second unit took 3,200 hours to complete and the cost for materials and equipment usage is $21,000. Labor cost is given as $18 per hour.

Determine the last unit (22^nd unit) cost to build:

$\begin{array}{c}\text{Labor learning rate}=\frac{3,200}{4,000}\\ =80\%\end{array}$

$\begin{array}{c}\text{Material learning rate}=\frac{21,000}{30,000}\\ =70\%\end{array}$

$\begin{array}{c}{\text{Labor cost for 22}}^{\text{nd}}\text{ unit}=4,000\times 0.3697\times \$18\\ =\$26,618.40\end{array}$

$\begin{array}{c}{\text{Machine cost for 22}}^{\text{nd}}\text{ unit}=30,000\times 0.2038\\ =\$6,114.00\end{array}$

$\begin{array}{c}{\text{Total amount for 22}}^{\text{nd}}\text{ unit}=\$26,618.40+\$6,114.00\\ =\$32,732.40\end{array}$

Hence, the last unit cost is $32,732.40.

b)

Summary Introduction

To determine: The average time for the 20 missile guidance controls.

Explanation of Solution

Given information:

It is given that first unit took 4,000 hours to complete and the cost for materials and equipment usage is $30,000. Second unit took 3,200 hours to complete and the cost for materials and equipment usage is $21,000. Labor cost is given as $18 per hour.

Determine the average time for the 20 missile guidance controls:

$\begin{array}{c}\begin{array}{l}\text{Labor cost for}\\ \text{20 more units}\end{array}\}=\left(\begin{array}{l}\text{Cumulative value for 22 units}-\\ \text{Cumulative value for 2 units}\end{array}\right)\times \left(\begin{array}{l}\text{Time to produce}\\ \text{first unit}\end{array}\right)\\ =\left(11.230-1.800\right)\times 4,000\\ =37,720\end{array}$

$\begin{array}{c}\text{Average labor time}=\frac{\text{Labor time for 20 more units}}{20}\\ =\frac{37,720}{20}\\ =1,886\text{ hours}\end{array}$

c)

Summary Introduction

To determine: The average cost for guidance control for the 20 in the contract.

Explanation of Solution

Given information:

It is given that first unit took 4,000 hours to complete and the cost for materials and equipment usage is $30,000. Second unit took 3,200 hours to complete and the cost for materials and equipment usage is $21,000. Labor cost is given as $18 per hour.

Determine average cost for guidance control for the 20 in the contract:

$\begin{array}{c}\begin{array}{l}\text{Labor cost for}\\ \text{20 more units}\end{array}\}=\left(\begin{array}{l}\text{Cumulative value for 22 units}-\\ \text{Cumulative value for 2 units}\end{array}\right)\times \left(\begin{array}{l}\text{Time to produce}\\ \text{first unit}\end{array}\right)\\ =\left(11.230-1.800\right)\times 4,000\\ =37,720\end{array}$

$\begin{array}{c}\text{Average labor cost}=\frac{\text{Labor time for 20 more units}}{20}\times \$18\\ =\frac{37,720}{20}\times \$18\\ =\$33,948\end{array}$

$\begin{array}{c}\begin{array}{l}\text{Material cost for}\\ \text{20 more units}\end{array}\}=\left(\begin{array}{l}\text{Cumulative value for 22 units}-\\ \text{Cumulative value for 2 units}\end{array}\right)\times \left(\begin{array}{l}\text{Material cost for}\\ \text{first unit}\end{array}\right)\\ =\left(7.819-1.700\right)\times \$30,000\\ =\$183,570\end{array}$

$\begin{array}{c}\text{Average cost}=\frac{\text{Material cost for 20 more units}}{20}\\ =\frac{\$183,570}{20}\\ =\$9,178.50\end{array}$

Determine the average total cost:

$\begin{array}{c}\text{Average total cost}=\text{Average labor cost}+\text{Average material cost}\\ =\$33,948+\$9,178.50\\ =\$43,126.50\end{array}$