A-Level Further Maths · Decision Mathematics
Linear Programming
What is it
Linear programming finds the optimal (maximum or minimum) value of a linear objective function, subject to a set of linear constraints, typically solved by graphing the constraints and testing the vertices of the resulting feasible region.
Why it matters
Linear programming is genuinely used throughout business and industry to optimise resource allocation — from minimising manufacturing costs to maximising delivery efficiency — making this one of the most practically applied topics in the entire A-Level syllabus.
Exam tip
The optimal solution to a linear programming problem always occurs at a vertex of the feasible region, never inside it — testing the objective function at each vertex, rather than trying to reason about the whole region, is the reliable way to find the answer.
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