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

Mathematics in Manufacturing Labor Costs Material Costs Machine Cost Product Costs Profit Copyright Texas Education Agency (TEA)

Labor Cost the wages paid to the workers and other employees of the company Copyright Texas Education Agency (TEA)

Labor Cost The formula for figuring the salary is: hourly wage X hours worked = labor cost $7.00 X 40 hours = $ Copyright Texas Education Agency (TEA)

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 Copyright Texas Education Agency (TEA)

Material Cost The formula for figuring material cost is: raw material cost X amount used = material cost oak cost $3.20 per board foot project requires 12 board feet $3.20 X 12 = $38.40 Copyright Texas Education Agency (TEA)

Machine Cost The formula for figuring machine cost is: machine operating cost ÷ units produced = machine cost CNC Lathe operating cost per hour = $ units are produced in one hour $50.00 ÷ 575 = $0.09 per part Copyright Texas Education Agency (TEA)

Product Cost The formula for figuring product cost is labor cost + material cost + machine cost + overhead = product cost. labor cost per part = $1.50 material cost per part= $0.75 machine cost per part = $0.35 overhead = $0.12 Total cost=$2.72 Copyright Texas Education Agency (TEA)

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= $5.95 product cost=-$2.72 profit= $3.23 Copyright Texas Education Agency (TEA)

Measurement Units unit cost bolts, other single parts board footage lumber square footage sheet stock linear footage bar stock Copyright Texas Education Agency (TEA)

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 Copyright Texas Education Agency (TEA)

Board Footage measurement of solid lumber the standard unit is 1” thick by 12” wide and 12” long 12” 1” Copyright Texas Education Agency (TEA)

Board Footage (bd ft) The formula for finding board footage is: Thickness X Width X Length standard unit T X W X L 144 material measurements are all in inches Copyright Texas Education Agency (TEA)

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 Copyright Texas Education Agency (TEA)

Figuring Board Footage 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” Copyright Texas Education Agency (TEA)

Figuring Board Footage 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 Copyright Texas Education Agency (TEA)

Calculating Board Footage from a Plan Bill of Material Part Name QuantityThicknessWidthLengthBoard Footage 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. Copyright Texas Education Agency (TEA)

Foot Stool Plans A C B B Copyright Texas Education Agency (TEA)

Board Footage for Top of Foot Stool Bill of Material Part Name QuantityThicknessWidthLengthBoard Footage Top (A) 1 3/4 ” 12” 14” 1.17 bd ft ” 1” X 12” X 14” 144” 1.17 bd ft = = A Copyright Texas Education Agency (TEA)

Bill of Material Part Name QuantityThicknessWidthLengthBoard Footage Ends (B) 2¾” 10 ” 8” 1.11bd ft Board Footage for Ends of Foot Stool 1” X 12” X 14” 144” 1.11 bd ft = = 168” /2 B Copyright Texas Education Agency (TEA)

Board Footage for Rails of Foot Stool Bill of Material Part Name QuantityThicknessWidthLengthBoard Footage Rails (C) 2 ¾” 2 ”10 ½”.29 bd ft 1” X 2” X 10 ½” 144” 0.29 bd ft = = 21” / /4 2 C Copyright Texas Education Agency (TEA)

Bill of Material Part Name QuantityThicknessWidthLengthBoard Footage Top (A) 1 ¾” 12” 14”1.17 bd ft Ends (B) 2¾” 10” 8”1.11bd ft Rails (C) 2 ¾” 2” 10 ½”.29 bd ft Total Board Footage A+B+C= 2.37bd ft A C B B Foot Stool Exploded View and Bill of Material Exploded View Copyright Texas Education Agency (TEA)

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) Copyright Texas Education Agency (TEA)

Square Footage The formula for figuring square footage (sq ft) cost is: width X length one square foot W X L 144 Copyright Texas Education Agency (TEA)

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 = Copyright Texas Education Agency (TEA)

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 C B B C C PartQuantityWidthLengthSquare Footage A11’3’? B21’4’? C31’3’? Total Square Footage? Copyright Texas Education Agency (TEA)

Linear Footage (Ln ft) material sold by the foot – molding – bar stock – pipe Copyright Texas Education Agency (TEA)

Linear Footage Cost The formula for figuring linear footage cost is: price X feet used Copyright Texas Education Agency (TEA)

Linear Footage Cost ½” pipe cost $0.25 per foot project uses 5 feet of ½” pipe $0.25 X 5’ = $1.25 Copyright Texas Education Agency (TEA)

Resources Clip art from & office clip artwww.clipart.com Copyright Texas Education Agency (TEA)

Resources for Teachers Mathematics for Manufacturing By Bridge to Advanced Technology Education and Employment Mathematics for Manufacturing Copyright Texas Education Agency (TEA)