Linear Programming

i=1 ajixi ≤ bj for 1 ≤ j ≤ m We can also minimize instead of maximize. The function ∑n i=1 cixi is known as the objective function, and the m inequalities are known as constraints. A vector ~x = x1, . . . , xn is feasible if it satisfies all constraints. A linear program is feasible if there exists a feasible vector. A constraint ∑ i ajixi ≤ bj is tight for ~x if ∑ i ajixi = bj . The value of a vector ~x is ∑ i cixi. A linear program is bounded if its value is bounded over all feasible vectors. The coefficient matrix of the linear program is the m× n matrix A whose entries are aji.