Linear Programming Problem (L.P.P.)

Linear Programming is an optimization technique used across management, planning, production, transportation and many

other fields. It was developed during the Second World War to optimize the utilization of limited resources for maximum

returns, and today the same technique is used to minimize the cost of production or maximize profit whenever a business

or organisation faces problems of efficiently allocating limited resources — raw materials, man-power, machine time, and

their associated costs — among competing uses.

Formally, Linear Programming is a mathematical technique designed to help managers with planning and decision-making.

Programming problems of this kind are also called optimization problems: the mathematical programming involves

optimizing (either maximizing or minimizing) a certain function, called the objective function, subject to a given

set of conditions or restrictions known as constraints. The rest of this section makes these terms precise (7.2.1), …