Linear Programming Mind Map

A linear programming problem is formulated by choosing decision variables, writing a linear objective function such as Z = ax + by, and expressing all given conditions as linear constraints.

Underline words such as at most, at least, not more than, minimum, maximum, profit, cost, and requirement before writing inequalities.

The graphical method solves a two-variable LPP by drawing the constraint lines, shading the common feasible region, finding its corner points, and evaluating the objective function at those points.

After drawing each boundary line, test a simple point such as (0, 0) when it is not on the line to decide the correct half-plane.

A feasible region is bounded if it can be enclosed within a finite part of the plane; it is unbounded if it extends indefinitely in at least one direction.

For an unbounded region, do not stop after listing corner values. Check whether better objective values are possible in the open direction of the feasible region.

Application word problems use linear programming to model real situations such as diet planning, manufacturing, transport, and allocation of limited resources.

Make a small table of resource use per unit before writing constraints; it reduces sign errors and missing conditions.