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Mathematics in Optimization

Role of Mathematics in Other Spheres //

Last Edited/ Updated on March 5, 2012

In a large variety of situations, we come across the problems of choosing best alternatives among many, which are feasible under the given constraints. These are known as optimization problems. We encounter such problems in our day to day life, in the fields of commerce and engineering too. All these problems have one common feature: to know how to make the best use of the available resources. The discipline of knowledge that deals with these problems has come to be known as Operations Research. A large body of mathematical techniques is applicable in this discipline.

In what follows, we describe various optimization problems.

Diet Problem (Day to Day Life)

There are several kinds of food items in our daily intake. Each food item further contains definite amounts of essential components like carbohydrates, fats, minerals and vitamins etc. We wish to make a food menu, taking care of the minimum requirements of the essential components, which have a minimum cost too.

Transportation Problem (Commerce)

In certain situations of business, the need arises to transport goods from more than one source to a number of different destinations. We wish to carry out the transportation in a cost effective manner, that is, in a way to minimize the costs.

Noise Removal Problem (Engineering)

There is an algorithm for removing noise from music. This algorithm works on the basis of the fact that any sound signal is a wave that can be represented graphically and that it has both parts, corresponding to the musical voice and the noise. The algorithm makes use of an iterative procedure for the reduction of the noise. Thus we are able to minimize the noise part.

We deal with this algorithm in Audio Engineering.

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Role of Mathematics in Other Spheres //