fedAngl

1.

The Use of Mathematics
in Manufacturing
Sagirov Fedor
FN11-23B

2.

Mathematics is often called the "language of science," but it is equally the
backbone of modern manufacturing. From the assembly line of a car factory
to the printing of a microchip, mathematical principles ensure that products
are made efficiently, accurately, and cost-effectively. Without mathematics,
mass production would be chaotic, inconsistent, and economically
unfeasible.

3.

Optimization and Operations Research
One of the most critical uses of math is in optimizing production. Linear programming and
queuing theory help managers determine the ideal combination of resources (labour, machines,
raw materials) to maximize output or minimize costs. For example, math is used to calculate
the most efficient sequence of jobs on a single machine to reduce downtime (a problem known
as "job shop scheduling").
belt conveyor drawing

4.

Geometry and Precision Engineering (CAD/CAM)
Before any physical product is made, it is designed mathematically using Computer-Aided
Design (CAD) software. Geometry, trigonometry, and calculus define every curve, angle, and
hole of a 3D model. This model is then converted into machine code (G-code) using
Computer-Aided Manufacturing (CAM). The machine tool moves in precise Cartesian
coordinates (X, Y, Z axes) to cut, drill, or mill the part to within a tolerance of 0.001 mm.
inventor 2020 - 3D modeling basic

5.

Statistical Quality Control
Not every product can be tested, especially in high-volume production (e.g., screws, batteries).
Instead, manufacturers use statistics. By taking random samples and applying normal
distribution, control charts, and standard deviation, they can predict whether the entire batch is
within specifications. This is the basis of Six Sigma, a methodology that aims for only 3.4
defects per million opportunities.

6.

Supply Chain and Inventory Management
Mathematics determines how much to order and when to order it. The Economic Order
Quantity (EOQ) model uses algebra to find the perfect order size that minimizes total
inventory costs (holding vs. ordering costs). Furthermore, forecasting future demand relies on
time series analysis and regression models to prevent stockouts or overproduction.

7.

Process Simulation and Calculus
For complex processes like chemical mixing, metal forging, or plastic injection molding,
calculus is used to model how variables change over time. For instance, the rate of heat flow
(derivatives) during the cooling of a plastic part determines if the product will warp.
Manufacturers use differential equations to simulate the process digitally before cutting a
single piece of metal, saving millions in trial-and-error costs.
Computer-aided engineering

8.

Thank you for you attention