# Discuss the scope and role of linear programming in solving management problems

Most operations research studies involve the construction of a mathematical model. The model is a collection of logical and mathematical relationships that represents aspects of the situation under study. Meaning, Characteristics, Assumption and other Details Article shared by: Read this article to learn about linear programming! The technique of linear programming was formulated by a Russian mathematician L. But the present version of simplex method was developed by Geoge B.

Linear programming LP is an important technique of operations research developed for optimum utilization of resources. According to famous Economist Robbins, the resources land, labour, capital, materials, machines, etc.

But each resource have various alternative uses. The problem before any manager is to select only those alternatives which can maximize the profit or minimize the cost of production. The linear programming technique is used for selecting the best possible strategy from a number of alternatives.

Linear programming consists of two words: Thus, linear programming is a mathematical technique for allocating limited resources is optimum manner.

In the words of William M. All linear programming problems must have following five characteristics: In business problems the objective is generally profit maximization or cost minimization.

All constraints limitations regarding resources should be fully spelt out in mathematical form. The value of variables must be zero or positive and not negative.

For example, in the case of production, the manager can decide about any particular product number in positive or minimum zero, not the negative. The relationships between variables must be linear. The number of inputs and outputs need to be finite. In the case of infinite factors, to compute feasible solution is not possible.

LP has been considered an important tool due to following reasons: LP makes logical thinking and provides better insight into business problems. Manager can select the best solution with the help of LP by evaluating the cost and profit of various alternatives.

LP assists in making adjustments according to changing conditions. LP helps in solving multi-dimensional problems. LP approach suffers from the following limitations also: This technique could not solve the problems in which variables cannot be stated quantitatively. In some cases, the results of LP give a confusing and misleading picture.

For example, the result of this technique is for the purchase of 1. It is very difficult to decide whether to purchase one or two- machine because machine can be purchased in whole. LP technique cannot solve the business problems of non-linear nature. The factor of uncertainty is not considered in this technique.

This technique is highly mathematical and complicated. If the numbers of variables or contrains involved in LP problems are quite large, then using costly electronic computers become essential, which can be operated, only by trained personel.

Under this technique to explain clearly the objective function is difficult.In addition to treating the physical origins of the equations, this course focuses on solving evolution equations as initial value problems on unbounded domains (the Cauchy problem), and also on solving partial differential equations on bounded domains (boundary value problems).

Graphical Method for solving problems with two variables The graphical method for solving linear programming problems in two unknowns is as follows. 1. Define the variables 2. Define the constraints 3. Define the objective function (the function which is to be maximised or minimised) 4. Graph the feasible region. 5. This course is designed with an emphasis on applications of analytical tools in healthcare organizations. Combinations of lectures and discussions on different topics important to healthcare finance will enable students to develop analytical skills necessary to solve a variety of financial management problems.

Deterministic approaches (e.g., linear programming, nonlinear programming, and mixed-integer nonlinear programming, etc.) can provide general tools for solving optimization problems to obtain a global or an approximately global optimum.