Q.1.   What Is a Linear Programming Problem ? Discuss the Steps and Role of Linear Programming Is Solving Management Problems

Linear Programming is a mathematical technique useful for allocation of scarce or limited resources to several competing activities on the basis of given criterion of optimality.The usefulness of linear programming as a tool for optimal decision-making on resource allocation, is based on its applicability to many diversified decision problems. The effective use and application requires, as on its applicability to many diversified decision problems. The effective use and application requires, as a first step, the mathematical formulation of an LP model, when the problem is presented in words. Steps of linear programming model formulation are summarized as follows :
STEP 1 : Identify the Decision Variables a) Express each constraint in words. For this you should first see whether the constraint is of the form >/ (at least as large as), of the form \< (no larger than) or of the form = (exactly equal to)

b) You should then verbally express the objective function

c) Steps (a) and (b) should then allow you to verbally identify the decision variables

If there are several decision alternatives available , then in order to identify the decision variables you need to ask yourself the question – what decisions must be made in order to optimize the objective function ?

Having accomplished step 1(a) through (c) decide the symbolic notation for the decision variables and specify units of measurement. Such specification of units of measurement would help in interpreting the final solution of the LP problem .

STEP 2 : Identify the Problem Data

For solving a problem, we need to identify the problem data so as to provide the actual values for the decision variables. For