Advanced Topic 38 of 51 Math for Computing
Linear Programming
Optimizing a linear objective under linear constraints.
How it works
Maximize cᵀx subject to Ax ≤ b, x ≥ 0; the feasible region is a convex polytope and an optimum lies at a vertex; duality relates the primal and dual problems.
Where it is used
Scheduling, logistics.
Common pitfall
Integer constraints make it NP-hard (ILP).
Where it fits in the course
Linear Programming is topic 38 of 51 in Math for Computing, rated Advanced. It follows Lagrange Multipliers. The next topic is Simplex Method.
Practice and explore
- Open the interactive lesson, with a mini quiz.
- Take the Math for Computing quiz.
How to study this topic
- Read the explanation above and restate the definition in your own words.
- Open the interactive lesson and answer its mini quiz.
- Read the common pitfall, then write a short example that avoids it.
- Check your understanding in the Math for Computing quiz, and revisit the topic if you miss a question.
Frequently asked questions
What is Linear Programming?
Optimizing a linear objective under linear constraints. It belongs to Math for Computing and is an advanced-level topic.
Where do people use Linear Programming?
Scheduling, logistics.
What is the most common mistake with Linear Programming?
Integer constraints make it NP-hard (ILP).
What should I learn before this topic?
Start with Lagrange Multipliers, the topic just before it in Math for Computing.
How can I practice it?
Answer the mini quiz in the interactive lesson, then take the Math for Computing quiz.
Is Linear Programming hard to learn?
It is an Advanced topic. Expect to read the explanation more than once and to connect it with earlier topics. Working through a small example by hand helps most.
How long does it take to learn Linear Programming?
Most learners can read the explanation and finish the interactive lesson in under an hour. Fluency comes from applying the idea, so plan a few short practice sessions with the quiz.
Which topics are related to Linear Programming?
Lagrange Multipliers, Simplex Method, Convex Optimization are closely connected. The full list is in the related topics section of this page.
What should I study after Linear Programming?
Continue with Simplex Method, the next topic in Math for Computing.
Related topics
- Lagrange Multipliers (Math for Computing)
- Simplex Method (Math for Computing)
- Convex Optimization (Math for Computing)
- Numerical Methods (Math for Computing)
- Programming Paradigms (Languages & Compilers)
- Linear Search (Algorithms)
- Linear Regression (AI & Machine Learning)