Title OR handout.pdf ✅

2  Investment decisions  Project management. CHAPTER 2: LINEAR PROGRAMING (LP) 2.1. Basic Concepts in LP Linear programming deals with the optimization (maximization or minimization) of a function of variables known as objective function, subject to a set of linear equation and /or inequalities known as constraints.  The objective function may be profit, cost, production capacity, or any other measure of effectiveness which is to be obtained in the best possible or optimal manner  The constraints may be imposed by different resources such as market demand, production process and equipment, storage capacity, raw material availability, etc.  By linearity is meant a mathematical expression in which the expressions among the variables are linear. Definition: LP is a mathematical modelling technique useful for economic allocation of “scarce” or “limited” resources (such as labor, material, machine, time, warehouse, space, capital, etc.) to several competing activities (such as products, services, jobs, new equipment, projects etc.) on the basis of a given criterion of optimality. All organizations, big or small, have at their disposal, men, machines, money and materials, the supply of which may be limited. Supply of resources being limited, the management must find the best allocation of resources in order to maximize the profit or minimize the loss or utilize the production capacity to the maximum extent. Steps in formulation of LP model: 1. Identify activities (key decision variables). 2. Identify the objective function as a linear function of its decision variables. 3. State all resource limitations as linear equation or inequalities of its decision variables. 4. Add non-negative constraints from the consideration that negative values of the decision variables do not have any valid physical interpretation. 5. Use mathematical techniques to find all possible sets of values of the variables (unknowns) satisfying all the function 6. Select the particular set of values of variables obtained in step five that leads to the achievement of the objective function.  The result of the first four steps is called linear programming. The set of solutions obtained in step five is known as the set of feasible solutions and the solution finally selected in step six is called optimum (best) solution of the LP problem.  A typical linear programming has two step  The objective function  The constraints  Technical constraint, and  The non-negativity constraint