Chapter 22, Problem 21A

To determine

Each type of cost for all three jobs.

Answer to Problem 21A

Date $9/16$:

Rework percentage is $2.7\%$.

Scrap percentage is $3.6\%$.

Date $9/17$:

Rework percentage is $1.8\%$.

Scrap percentage is $3.0\%$.

Date $9/18$:

Rework percentage is $3.1\%$.

Scrap percentage is $2.0\%$.

Explanation of Solution

Given information:

Below table shows the total pieces manufactured along with rework and scrap defective pieces.

  

Calculation:

We have been given a table with details of total pieces manufactured along with defective pieces.

  

Now we need to find the individual defect percentage for each day. Total pieces manufactured will be base and number of defective pieces will be percentage.

As we know the proportion to find percentage is given as

  $\frac{P}{B}=\frac{R}{100}$   where, $P=\text{percentage, }B=\text{ base and }R=\text{rate}$

Date $9/16$:

Rework piece $=$$44$ i.e. $P=$$44$ and total manufactured piece $=$$1650$ i.e. $B=$$1650$.

Putting these value in standard proportion,

  $\begin{array}{l}\frac{P}{B}=\frac{R}{100}\\ \Rightarrow \frac{44}{1650}=\frac{R}{100}\text{ {Put }B=1650\text{ and }P=44\text{}}\\ \text{Applying cross multiplication,}\\ \Rightarrow 1650R=44\times 100\\ \Rightarrow R=\frac{44\times 100}{1650}\\ \Rightarrow R=2.6667\\ \Rightarrow R=2.7\text{ {Rounding off to 1 decimal places}}\end{array}$

Hence, the rework percentage is $2.7\%$.

Similarly, scrap piece $=$$59$ i.e. $P=$$59$ and total manufactured piece $=$$1650$ i.e. $B=$$1650$.

Putting these value in standard proportion,

  $\begin{array}{l}\frac{P}{B}=\frac{R}{100}\\ \Rightarrow \frac{59}{1650}=\frac{R}{100}\text{ {Put }B=1650\text{ and }P=59\text{}}\\ \text{Applying cross multiplication,}\\ \Rightarrow 1650R=59\times 100\\ \Rightarrow R=\frac{59\times 100}{1650}\\ \Rightarrow R=3.575757\\ \Rightarrow R=3.6\text{ {Rounding off to 1 decimal places}}\end{array}$

Hence, the scrap percentage is $3.6\%$.

Date $9/17$:

Rework piece $=$$29$ i.e. $P=$$29$ and total manufactured piece $=$$1596$ i.e. $B=$$1596$.

Putting these value in standard proportion,

  $\begin{array}{l}\frac{P}{B}=\frac{R}{100}\\ \Rightarrow \frac{29}{1596}=\frac{R}{100}\text{ {Put }B=1596\text{ and }P=29\text{}}\\ \text{Applying cross multiplication,}\\ \Rightarrow 1596R=29\times 100\\ \Rightarrow R=\frac{29\times 100}{1596}\\ \Rightarrow R=1.81704\\ \Rightarrow R=1.8\text{ {Rounding off to 1 decimal places}}\end{array}$

Hence, the rework percentage is $1.8\%$.

Similarly, scrap piece $=$$48$ i.e. $P=$$48$ and total manufactured piece $=$$1596$ i.e. $B=$$1596$.

Putting these value in standard proportion,

  $\begin{array}{l}\frac{P}{B}=\frac{R}{100}\\ \Rightarrow \frac{48}{1596}=\frac{R}{100}\text{ {Put }B=1596\text{ and }P=48\text{}}\\ \text{Applying cross multiplication,}\\ \Rightarrow 1596R=48\times 100\\ \Rightarrow R=\frac{48\times 100}{1596}\\ \Rightarrow R=3.0075\\ \Rightarrow R=3.0\text{ {Rounding off to 1 decimal places}}\end{array}$

Hence, the scrap percentage is $3.0\%$.

Date $9/18$:

Rework piece $=$$52$ i.e. $P=$$52$ and total manufactured piece $=$$1685$ i.e. $B=$$1685$.

Putting these value in standard proportion,

  $\begin{array}{l}\frac{P}{B}=\frac{R}{100}\\ \Rightarrow \frac{52}{1685}=\frac{R}{100}\text{ {Put }B=1685\text{ and }P=52\text{}}\\ \text{Applying cross multiplication,}\\ \Rightarrow 1685R=52\times 100\\ \Rightarrow R=\frac{52\times 100}{1685}\\ \Rightarrow R=3.08605\\ \Rightarrow R=3.1\text{ {Rounding off to 1 decimal places}}\end{array}$

Hence, the rework percentage is $3.1\%$.

Similarly, scrap piece $=$$34$ i.e. $P=$$34$ and total manufactured piece $=$$1685$ i.e. $B=$$1685$.

Putting these value in standard proportion,

  $\begin{array}{l}\frac{P}{B}=\frac{R}{100}\\ \Rightarrow \frac{34}{1685}=\frac{R}{100}\text{ {Put }B=1685\text{ and }P=34\text{}}\\ \text{Applying cross multiplication,}\\ \Rightarrow 1685R=34\times 100\\ \Rightarrow R=\frac{34\times 100}{1685}\\ \Rightarrow R=2.01750\\ \Rightarrow R=2.0\text{ {Rounding off to 1 decimal places}}\end{array}$

Hence, the scrap percentage is $2.0\%$.

Thus,

Date $9/16$:

Rework percentage is $2.7\%$.

Scrap percentage is $3.6\%$.

Date $9/17$:

Rework percentage is $1.8\%$.

Scrap percentage is $3.0\%$.

Date $9/18$:

Rework percentage is $3.1\%$.

Scrap percentage is $2.0\%$.