Linear Programming — Part 2: Optimal solutions by the corner point method: visual lesson, ISC Class 12 Mathematics

Lesson

Linear Programming, Part 2

The best plan is found at a corner of the feasible region.

In this lesson you will

Explain why the optimum of a linear objective lies at a corner point
Solve problems by the corner point method
Use the half-plane test on unbounded regions and recognise when no optimum exists
Recognise infinitely many optimal solutions

Part 2 at a glance.

Diagram

Parallel lines $4x + 5y = k$: the last point touched is a corner.

Lines $ax + by = k$ for different $k$ are parallel; the last point of the region they touch is a corner.

Concept

Bounded: compare corner values. Unbounded: also test the half-plane.

The corner point method.