Understanding Linear Programming and Optimization
Linear programming (LP) is a mathematical optimization method used to determine the best possible outcome (such as maximizing profit or minimizing cost) in a given mathematical model, subject to a set of linear constraints. Widely used in business, logistics, manufacturing, and economics, linear programming helps managers allocate limited resources (like time, labor, raw materials, or capital) to achieve maximum efficiency.
A linear programming problem consists of a linear objective function that we want to optimize, and a set of linear inequality or equality constraints that restrict the decision variables. Because the relationships are linear, the set of all feasible solutions forms a convex polygon called the feasible region. According to the Fundamental Theorem of Linear Programming, the optimal solution always occurs at one of the corner points (vertices) of this feasible region.
This calculator solves 2-variable linear programming problems using the graphical corner-point method: it evaluates the coordinates of every vertex of the feasible region formed by two constraints, checks each against the objective function, and identifies the optimal coordinates and maximum/minimum value.