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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?
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Mathematics in Manufacturing
• Labor Costs • Material Costs• Machine Cost• Product Costs• Profit
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Labor Cost
• the wages paid to the workers and other employees of the company
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Labor Cost
The formula for figuring the salary is:hourly wage X hours worked = labor cost
$7.00 X 40 hours = $280.00
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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
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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
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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
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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
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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
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Measurement Units
unit cost bolts, other single parts board footage lumbersquare footage sheet stocklinear footage bar stock
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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
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Board Footage
• measurement of solid lumber • the standard unit is 1” thick by 12” wide and
12” long
12”
12”
1”
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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
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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”
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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
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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.
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Foot Stool Plans
A
CB
B
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Board Footage forTop of Foot Stool
Bill of Material
PartName
Quantity Thickness Width Length BoardFootage
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
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Bill of Material
PartName
Quantity Thickness Width Length BoardFootage
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
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Board Footage forRails of Foot Stool
Bill of Material
PartName
Quantity Thickness Width Length BoardFootage
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
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Bill of Material
PartName
Quantity Thickness Width Length BoardFootage
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
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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)
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Square Footage
• The formula for figuring square footage (sq ft) cost is:
width X lengthone square foot
W X L144
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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=
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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 ?
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Linear Footage(Ln ft)
• material sold by the foot– molding– bar stock– pipe
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Linear Footage Cost
• The formula for figuring linear footage cost is:
price X feet used
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Linear Footage Cost
½” pipe cost $0.25 per footproject uses 5 feet of ½” pipe
$0.25 X 5’ = $1.25
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Resources
• Clip art from www.clipart.com & office clip art
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Resources for Teachers
• Mathematics for Manufacturing By Bridge to Advanced Technology Education and Employment
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