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Linear Programming (LP) is an important quantitative technique used in managerial decision-making to determine the best possible allocation of limited resources among competing activities. It is based on the idea that managerial problems can be expressed in terms of a mathematical model containing an objective function, decision variables, constraints, and non-negativity conditions. From the managerial and systems approach, Linear Programming is useful because it views an organisation as an interconnected system in which resources, activities, departments, and objectives are related to one another. The main purpose of Linear Programming is optimisation. Management generally has to make decisions under conditions of scarcity. Resources such as capital, labour, raw materials, machine hours, storage space, transportation capacity, and time are limited, while the organisation may have several alternative uses for these resources. LP helps management decide how these scarce resources should be distributed so that profit is maximised, cost is minimised, output is maximised, or another organisational objective is achieved. A Linear Programming model consists of several basic components. The first is the decision variables. These represent the quantities that management has to determine. For example, if a company produces two products, X and Y, the quantities of X and Y produced can be represented by decision variables x and y. The second component is the objective function. It expresses the managerial goal mathematically. If the company wants to maximise profit, the objective function may be written as Maximise Z = 50x + 40y, where 50 and 40 represent the profit per unit of the two products. The third component consists of constraints. Constraints represent the limitations imposed on available resources or ______ ____ _________ _____ ______ ____ _______.
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