Principles of Manufacturing M anufacturing Mathematics Copyright Texas Education Agency (TEA)

Principles of ManufacturingManufacturing Mathematics

Copyright Texas Education Agency (TEA)

What Type of Mathematics is Used in Manufacturing?

How much money did I make? How much does it cost to make a bookshelf?

How much wood does it take to make a foot stool?


Mathematics in Manufacturing

• Labor Costs • Material Costs• Machine Cost• Product Costs• Profit


Labor Cost

• the wages paid to the workers and other employees of the company


Labor Cost

The formula for figuring the salary is:hourly wage X hours worked = labor cost

$7.00 X 40 hours = $280.00


Costs

• material cost: cost of the material used in making the product

• machine cost: standard cost of operating a machine

• product cost: cost of producing the finished product


Material Cost

• The formula for figuring material cost is: raw material cost X amount used = material cost

oak cost $3.20 per board footproject requires 12 board feet

$3.20 X 12 = $38.40


Machine Cost

• The formula for figuring machine cost is: machine operating cost ÷ units produced = machine cost

CNC Lathe operating cost per hour = $50.00575 units are produced in one hour

$50.00 ÷ 575 = $0.09 per part


Product Cost

• The formula for figuring product cost is labor cost + material cost + machine cost +

overhead = product cost.labor cost per part = $1.50material cost per part = $0.75machine cost per part = $0.35overhead = $0.12Total cost = $2.72


Profit

• the money made after paying the wages and overhead of manufacturing the product

• The formula for profit is: selling price – product cost = profit

selling price = $5.95product cost = -$2.72

profit = $3.23


Measurement Units

unit cost bolts, other single parts board footage lumbersquare footage sheet stocklinear footage bar stock


Unit Cost• ¼” X 2” bolts could be sold in a box • The formula for the cost of one bolt:

box price ÷ number of bolts in the box$5.99 per box

100 bolts in box$5.99 ÷ 100 = $05.9

• some things are sold by the individual piece– switches– connectors– hardware


Board Footage

• measurement of solid lumber • the standard unit is 1” thick by 12” wide and

12” long

12”

12”

1”


Board Footage(bd ft)

The formula for finding board footage is:

Thickness X Width X Length standard unit

T X W X L144

material measurements are all in inches


Figuring Board Footage

• thickness less than 1” is figured at 1” and thickness over 1” is calculated at true size

• a board ¾” thick is figured at 1” in the formula• a board 1 ½” thick is figured at 1 ½” in the

formula



• measure the size of the piece of wood in inches

1 ½ bd ft = =

6

3/4

36

1” X 6” X 36” 216”

1” X 12” X 12” 144”



A cutting board is measured at 1 ¾” thick by 12” wide by 16” long. What is the board footage of the cutting board?

1.75” X 12” X 16” 336” 1” X 12” X 12” 144”

Remember: any thickness (T) over 1” is calculated at true size

= = 2.33 bd ft


Calculating Board Footage from a Plan

Bill of MaterialPartName

Quantity Thickness Width Length BoardFootage

Plans show sizes of the parts used to make the project. The measurements are taken from the plans and written in a chart called a bill of materials. These measurements are then used to calculate the board footage.


Foot Stool Plans

A

CB

B


Board Footage forTop of Foot Stool

Bill of Material

PartName


Top (A) 1 3/4 ” 12” 14” 1.17 bd ft

14

12

168”1” X 12” X 14”

144”144”

1.17 bd ft= =

A


Bill of Material

PartName


Ends (B) 2 ¾” 10 ” 8” 1.11bd ft

Board Footage forEnds of Foot Stool

1” X 12” X 14”

144”144”

1.11 bd ft= =168”

10

2 1/2 2 1/2 2 1/2

B


Board Footage forRails of Foot Stool

Bill of Material

PartName


Rails (C)2 ¾” 2 ” 10 ½” .29 bd ft

1” X 2” X 10 ½”

144”144”

0.29 bd ft= =21”

2

10 1/2

1

8

3 1/4 3 1/4 2

C


Bill of Material

PartName


Top (A) 1 ¾” 12” 14” 1.17 bd ftEnds (B) 2 ¾” 10” 8” 1.11bd ft Rails (C) 2 ¾” 2” 10 ½” .29 bd ftTotal Board Footage A+B+C= 2.37bd ft

A

CB

B

Foot StoolExploded View and Bill of Material Exploded View


Square Footage(sq ft)

• used to purchase sheet material such as plywood, sheet metal, and plastic sheets

• the width and length is measured • thickness is not figured in to the formula • the material is produced in a specific thickness• example: (3/4 inch plywood, ¼ plastic or 16

gauge sheet metal)


Square Footage

• The formula for figuring square footage (sq ft) cost is:

width X lengthone square foot

W X L144


Square Footage

• The side of a kitchen cabinet is made of ¾” oak plywood. The cabinet size is 24” deep and 34” tall. How many square feet are in the cabinet side?

24” X 36” 144”

6 sq ft=


Square Footage• A bookcase is 1 foot

deep, 3 feet wide and 4 feet tall. How many square feet of plywood are in the bookcase?

4’

1’

3’

A

CB

B

C

C

Part Quantity Width Length Square Footage

A 1 1’ 3’ ?

B 2 1’ 4’ ?

C 3 1’ 3’ ?

Total Square Footage ?


Linear Footage(Ln ft)

• material sold by the foot– molding– bar stock– pipe


Linear Footage Cost

• The formula for figuring linear footage cost is:

price X feet used


Linear Footage Cost

½” pipe cost $0.25 per footproject uses 5 feet of ½” pipe

$0.25 X 5’ = $1.25


Resources

• Clip art from www.clipart.com & office clip art


http://www.clipart.com/

Resources for Teachers

• Mathematics for Manufacturing By Bridge to Advanced Technology Education and Employment


http://www.uic.edu/cuppa/techbridge/PDF/MathforManufacturing_100300.PDF

Documents

Principles of Manufacturing M anufacturing Mathematics Copyright Texas Education Agency (TEA)