Maximisation and Minimisation Applications

The corner-point method turns real commercial questions into a short, repeatable calculation. Two families of problem recur throughout the Std XII (Commerce) course.

Maximisation (profit / output)

Here the objective is a profit or revenue to be made as large as possible, and the constraints are resource ceilings ($\le$): machine hours available, raw material in stock, a budget not to be exceeded. The feasible region is usually bounded, so the maximum sits at a corner and is found directly.

Minimisation (cost / requirement)

Here the objective is a cost to be made as small as possible, and the constraints are usually requirements that must be met ($\ge$): a minimum amount of each nutrient in a diet, a minimum output to fulfil an order. The feasible region is often unbounded, so the open-half-plane check of Section 3 is applied before declaring the minimum.