Linear Programming — Class 12 Mathematics

Linear programming finds the optimal value of a linear objective function subject to linear constraints. A typical problem maximises or minimises subject to inequalities such as together with the non-negativity constraints . The set of points satisfying all constraints is the feasible region, a convex polygon (possibly unbounded). The key result is that an optimal value of , when it exists, occurs at a corner (vertex) of the feasible region. The Corner Point Method therefore evaluates at each vertex and selects the largest or smallest value. For a bounded feasible region both a maximum and a minimum exist; for an unbounded region an optimum may fail to exist, which must be checked. The chapter solves such problems graphically in two variables.