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Applied Mathematics · Quick Reference
Operations Research Cheat Sheet
In one line: operations research applies mathematical modeling and optimization to real-world decision-making — helping organizations run more efficiently by finding the best way to allocate limited resources.
Key Ideas
1What is Operations Research?. The application of mathematical methods (especially optimization and modeling) to help organizations make better decisions about resources, logistics, and scheduling.
2Linear Programming in OR. A core tool: maximizing or minimizing an objective (like cost or profit) subject to a set of linear constraints (like limited labor hours or materials).
3The Feasible Region. The set of all possible solutions that satisfy every constraint simultaneously, often visualized as a shaded region on a graph.
4Queuing Theory. The mathematical study of waiting lines, used to analyze and improve systems like customer service lines, call centers, or network traffic.
5The Transportation Problem. A classic OR problem: finding the cheapest way to ship goods from multiple suppliers to multiple destinations while meeting demand and supply limits.
Worked Examples
A factory can make at most 40 chairs and 30 tables per week due to labor limits: chairs take 2 hours, tables take 3 hours, with 100 hours available. Write the labor constraint as an inequality.
2c + 3t <= 100
A company earns $30 profit per chair and $50 profit per table. Write the objective function to maximize profit.
Maximize P = 30c + 50t
Why does the optimal solution to a linear programming problem occur at a corner of the feasible region rather than somewhere in the middle?
Because a linear objective function's extreme values always occur at the boundary/corners of a convex feasible region
Practice Yourself
A constraint says 3x+2y <= 60. Is the point (10,10) feasible?
Yes, 3(10)+2(10)=50, which is <= 60
What does 'operations research' primarily apply mathematics to?
Improving real-world decision-making about resources and logistics
What kind of region contains all valid solutions to a set of constraints?
The feasible region
What OR topic studies waiting lines?
Queuing theory