Chapter 7, Problem 15OQ

a)

Summary Introduction

To draw: A process flow diagram and determine the processing capacity of the whole process.

Process capacity:

Process capacity is the maximum level of output can be possibly obtained through a specific machine of the production line.

Explanation of Solution

Given information:

Hours     = 8 per day

Days     = 5 per week.

Cost of purchasing parts:

Part A     = 40 cents per piece.

Part B     = 35 cents per piece

Part C     = 15 cents per piece.

Production output:

Assembly line 1         = 140 components per hour.

Operational drill machines     = 3

Drilling Part C         = 50 parts per hour.

Final assembly line         = 160 components per hour.

Cost of production:

Assembly labor             = 30 cents per part.

Drilling labor                 = 15 cents per part.

Cost of electricity             = 1 cent per part.

Total overhead cost             = $1,200 per week,

Depreciation cost for equipment     = $30 per week

Process flow diagram:

Calculation of capacity:

$\begin{array}{c}\text{Assembly line 1}=\text{Units per hour}\times \text{Hours per day}\times \text{Days per week}\\ =140\times 8\times 5\\ =5,600\text{ units per week}\end{array}$

$\begin{array}{c}\text{Drill machines}=\text{Number of drill machines}\times \text{Parts per hour}\times \text{Hours per day}\times \text{Days per week}\\ =3\times 50\times 8\times 5\\ =6,000\text{ units per week}\end{array}$

$\begin{array}{c}\text{Final Assembly line}=\text{Units per hour}\times \text{Hours per day}\times \text{Days per week}\\ =160\times 8\times 5\\ =6,400\text{ units per week}\end{array}$

The overall capacity of the process will be equal to the activity with the lowest individual capacity.

Hence, the capacity of the process is 5,600 units per week.

b)

Summary Introduction

To calculate: The new process capacity and identify the operation that limits the capacity.

Explanation of Solution

Given information:

Hours             = 16 per day

Days             = 5 per week.

Number of shifts     = 2 per day

Cost of purchasing parts:

Part A     = 40 cents per piece.

Part B     = 35 cents per piece

Part C     = 15 cents per piece.

Production output:

Assembly line 1         = 140 components per hour.

Operational drill machines     = 4

Drilling hours             = 8 per day

Drilling Part C         = 50 parts per hour.

Final assembly line         = 160 components per hour.

Cost of production:

Assembly labor             = 30 cents per part.

Drilling labor                 = 15 cents per part.

Cost of electricity             = 1 cent per part.

Total overhead cost             = $1,200 per week,

Depreciation cost for equipment     = $30 per week

Calculation of capacity:

$\begin{array}{c}\text{Assembly line 1}=\text{Units per hour}\times \text{Hours per day}\times \text{Days per week}\\ =140\times 16\times 5\\ =11,200\text{ units per week}\end{array}$

$\begin{array}{c}\text{Drill machines}=\text{Number of drill machines}\times \text{Parts per hour}\times \text{Hours per day}\times \text{Days per week}\\ =4\times 50\times 8\times 5\\ =8,000\text{ units per week}\end{array}$

$\begin{array}{c}\text{Final Assembly line}=\text{Units per hour}\times \text{Hours per day}\times \text{Days per week}\\ =160\times 16\times 5\\ =12,800\text{ units per week}\end{array}$

The overall capacity of the process will be equal to the activity with the lowest individual capacity. The capacity of the process is 8,000 units per week.

The drilling operation only works for 8 hours in a day limiting the overall capacity.

c)

Summary Introduction

To calculate: The new process capacity and identify the operation that limits the capacity.

Explanation of Solution

Given information:

Hours for assembly line 1    = 16 per day

Hours of Final assembly line     = 12 per day

Days                 = 5 per week.

Number of shifts         = 2 per day

Cost of purchasing parts:

Part A     = 40 cents per piece.

Part B     = 35 cents per piece

Part C     = 15 cents per piece.

Production output:

Assembly line 1         = 140 components per hour.

Operational drill machines     = 5

Drilling hours             = 8 per day

Drilling Part C         = 50 parts per hour.

Final assembly line         = 160 components per hour.

Cost of production:

Assembly labor             = 30 cents per part.

Drilling labor                 = 15 cents per part.

Cost of electricity             = 1 cent per part.

Total overhead cost             = $1,200 per week,

Depreciation cost for equipment     = $30 per week

Calculation of capacity:

$\begin{array}{c}\text{Assembly line 1}=\text{Units per hour}\times \text{Hours per day}\times \text{Days per week}\\ =140\times 16\times 5\\ =11,200\text{ units per week}\end{array}$

$\begin{array}{c}\text{Drill machines}=\text{Number of drill machines}\times \text{Parts per hour}\times \text{Hours per day}\times \text{Days per week}\\ =5\times 50\times 8\times 5\\ =10,000\text{ units per week}\end{array}$

$\begin{array}{c}\text{Final Assembly line}=\text{Units per hour}\times \text{Hours per day}\times \text{Days per week}\\ =160\times 12\times 5\\ =9,600\text{ units per week}\end{array}$

The overall capacity of the process will be equal to the activity with the lowest individual capacity. The capacity of the process is 9,600 units per week.

The final assembly line only works for 4 hours in the second shift limiting the overall capacity.

d)

Summary Introduction

To calculate: The cost per unit for the previous two calculated capacities.

Explanation of Solution

Given information:

Hours for assembly line 1    = 16 per day

Hours of Final assembly line     = 12 per day

Days                 = 5 per week.

Number of shifts         = 2 per day

Cost of purchasing parts:

Part A     = 40 cents per piece.

Part B     = 35 cents per piece

Part C     = 15 cents per piece.

Production output:

Assembly line 1         = 140 components per hour.

Operational drill machines     = 5

Drilling hours             = 8 per day

Drilling Part C         = 50 parts per hour.

Final assembly line         = 160 components per hour.

Cost of production:

Assembly labor             = 30 cents per part.

Drilling labor                 = 15 cents per part.

Cost of electricity             = 1 cent per part.

Total overhead cost             = $1,200 per week,

Depreciation cost for equipment     = $30 per week

Calculation of cost per unit when the capacity is 8,000 and 9,600 units:

Formula:

e)

Summary Introduction

To calculate: The break-even number of units.

Explanation of Solution

Given information:

Product selling price             = $4 per unit.

Fixed cost per drilling machine     = $30,000

Output per week             = 8,000 parts

Number of drilling machines         = 4

Product buying price             = $3 per unit

Calculation of break-even number of units:

Let ‘x’ be the number of units each option will produce.

The cost of buying the unit becomes

$\text{Total cost}=3x$ .

When the firm decides to manufacture the part, it incurs a fixed for each of the drilling machines which will be:

$\begin{array}{c}\text{Fixed cost for drilling machine}=4\text{ machines}\times 30,000\text{ per machine}\\ =\$120,000\end{array}$

The cost per unit for manufacturing as calculated before is $1.81.

Therefore the total cost of manufacturing the part is:

$\text{Total cost}=120,000+3x$

The total cost of buying and manufacturing is equated to each other to calculate the break-even units as shown below:

$\begin{array}{c}3x=120,000+1.81x\\ 3x-1.81x=120,000\\ x=\frac{120,000}{1.19}\\ =100,840\text{ units}\end{array}$

The break-even units are 100,840 units.