Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 24, Problem 41A
To determine

Each type of cost for all three jobs.

Expert Solution & Answer
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Answer to Problem 41A

Job 1:

Labor cost percentage is 47%.

Material cost percentage is 22%.

Overhead cost percentage is 31%.

Job 2:

Labor cost percentage is 32%.

Material cost percentage is 37%.

Overhead cost percentage is 31%.

Job 3:

Labor cost percentage is 42%.

Material cost percentage is 31%.

Overhead cost percentage is 27%.

Explanation of Solution

Given information:

Manufacturing cost consists of labor costs, material cost and overhead cost. Total manufacturing cost for job 1,2 and 3 is given as below.

  Mathematics For Machine Technology, Chapter 24, Problem 41A

Calculation:

Components of manufacturing cost is given as below.

    JobLabor CostMaterial costOverhead costTotal cost
    1$1890$875$1240$4005
    2.$930$1060$880$2870
    3.$2490$1870$1600$5960

Now we need to find the individual cost percentage for each job. Total cost will be base and individual costs will be percentage.

As we know the proportion to find percentage is given as

  PB=R100   where, P=percentage, B= base and R=rate

Job 1:

Labor cost =$1890 i.e. P=$1890 and total manufacturing cost =$4005 i.e. B=$4005.

Putting these value in standard proportion,

  PB=R10018904005=R100                           {Put B=4005 and P=1890}Applying cross multiplication,4005R=1890×100R=1890×1004005R=47.191R=47                                    {Rounding off to nearest whole number}

Hence, the labor cost percentage is 47%.

Similarly,

Material cost =$875 i.e. P=$875 and total manufacturing cost =$4005 i.e. B=$4005.

Putting these value in standard proportion,

  PB=R1008754005=R100                           {Put B=4005 and P=875}Applying cross multiplication,4005R=875×100R=875×1004005R=21.84769R=22                                    {Rounding off to nearest whole number}

Hence, the material cost percentage is 22%.

Again,

Overhead cost =$1240 i.e. P=$1240 and total manufacturing cost =$4005 i.e. B=$4005

Putting these value in standard proportion,

  PB=R10012404005=R100                           {Put B=4005 and P=1240}Applying cross multiplication,4005R=1240×100R=1240×1004005R=30.96129R=31                                    {Rounding off to nearest whole number}

Hence, the Overhead cost percentage is 31%.

Job 2:

Labor cost =$930 i.e. P=$930 and total manufacturing cost =$2870 i.e. B=$2870.

Putting these value in standard proportion,

  PB=R1009302870=R100                           {Put B=2870 and P=930}Applying cross multiplication,2870R=930×100R=930×1002870R=32.4041R=32                                    {Rounding off to nearest whole number}

Hence, the labor cost percentage is 32%.

Similarly,

Material cost =$1060 i.e. P=$1060 and total manufacturing cost =$2870 i.e. B=$2870.

Putting these value in standard proportion,

  PB=R10010602870=R100                           {Put B=2870 and P=1060}Applying cross multiplication,2870R=1060×100R=1060×1002870R=36.93379R=37                                    {Rounding off to nearest whole number}

Hence, the material cost percentage is 37%.

Again,

Overhead cost =$880 i.e. P=$880 and total manufacturing cost =$2870 i.e. B=$2870

Putting these value in standard proportion,

  PB=R1008802870=R100                           {Put B=2870 and P=880}Applying cross multiplication,2870R=880×100R=880×1002870R=30.6620R=31                                    {Rounding off to nearest whole number}

Hence, the Overhead cost percentage is 31%.

Job 3:

Labor cost =$2490 i.e. P=$2490 and total manufacturing cost =$5960 i.e. B=$5960.

Putting these value in standard proportion,

  PB=R10024905960=R100                           {Put B=5960 and P=2490}Applying cross multiplication,5960R=2490×100R=2490×1005960R=41.7785R=42                                    {Rounding off to nearest whole number}

Hence, the labor cost percentage is 42%.

Similarly,

Material cost =$1870 i.e. P=$1870 and total manufacturing cost =$5960 i.e. B=$5960.

Putting these value in standard proportion,

  PB=R10018705960=R100                           {Put B=5960 and P=1870}Applying cross multiplication,5960R=1870×100R=1870×1005960R=31.3758R=31                                    {Rounding off to nearest whole number}

Hence, the material cost percentage is 31%.

Again, Overhead cost =$1600 i.e. P=$1600 and total manufacturing cost =$5960 i.e. B=$5960.

Putting these value in standard proportion,

  PB=R10016005960=R100                           {Put B=5960 and P=1600}Applying cross multiplication,5960R=1600×100R=1600×1005960R=26.845637R=27                                    {Rounding off to nearest whole number}

Hence, the overhead cost percentage is 27%.

Thus,

Job 1:

Labor cost percentage is 47%.

Material cost percentage is 22%.

Overhead cost percentage is 31%.

Job 2:

Labor cost percentage is 32%.

Material cost percentage is 37%.

Overhead cost percentage is 31%.

Job 3:

Labor cost percentage is 42%.

Material cost percentage is 31%.

Overhead cost percentage is 27%.

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Chapter 24 Solutions

Mathematics For Machine Technology

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