Topic summary · Decision maths (D1)
Linear Programming summary
Linear programming optimises a linear objective under linear inequalities. Graph the feasible region and test vertices.
Files: D1-Linear Programming.pdf · D1-Linear Programming answers.pdf · free public downloads · diagrams in the PDFs
Key learning points
- Translate wording into inequality constraints (include non-negativity).
- The feasible region is an intersection of half-planes.
- A linear objective attains its optimum at a vertex.
- Integer requirements may need checking nearby lattice points.
Worked example 1 — Vertices
Why evaluate the objective at each vertex?
Working
Compare values to select the required max or min.
Worked example 2 — Translate wording into inequality constraints (include
Use this method from the Linear Programming sheet: Translate wording into inequality constraints (include non-negativity).
Working
Each key learning point matches a question type on the printable worksheet.
Worked example 3 — The feasible region is an intersection of half-planes
Use this method from the Linear Programming sheet: The feasible region is an intersection of half-planes.
Working
Each key learning point matches a question type on the printable worksheet.
Worked example 4 — A linear objective attains its optimum at a vertex
Use this method from the Linear Programming sheet: A linear objective attains its optimum at a vertex.
Working
Each key learning point matches a question type on the printable worksheet.
Worked example 5 — Integer requirements may need checking nearby lattice
Use this method from the Linear Programming sheet: Integer requirements may need checking nearby lattice points.
Working
Each key learning point matches a question type on the printable worksheet.
Scaffolded Learning Sheet and answers (PDFs)
This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.