Uses of calculus in business - Research Paper Example

BUSINESS MATH al Affiliation) Introduction Mathematics is widely applied in various commercial and business exercises in the world; commercial enterprises have applied different facets of mathematics ranging from management of inventories to the management of accounting used in sales as well as in processes that entail forecasting sales (Thompson, 2011). Various aspects of mathematics used in business enterprises include algebra, probability as well as calculus that have been widely used in the contemporary society.

How Calculus is applied in BusinessThe concept of calculus is a dimension of mathematics that is basically used to assess certain changes in a mathematical manner. Researchers have indicated that calculus is one of the modern facets of mathematics that has been effectively used to assess certain changes or arrive at certain decisions in the current business world.The use of directives to calculate certain aspects of business has been evident in various ways. People engaged in undertaking real estate business have applied the concept of derivatives in calculus to determine their overall income for instance:If a land owner with a complex apartment with 250 houses, each house rented on a monthly rate of y.

How many houses should the owner of the apartment rent in order to ensure that he maximizes his income?Note: The monthly rental apartment is derived as: P(y) = -8y2 + 3200y – 80,000The solution to this problemThe main concern in this case is to maximize the income by determining the number of maximum houses to be rented meaning; y ranges between 0 and 250 whereby: 0≤ y ≤ 250. In order to determine the solution, it is important to determine critical points that occur between 0 and 250. Therefore:P(y) = 16y + 3200 leading to 3200 – 16y = 0, this results to y = 3200÷16 = 200Owing to the fact that the profit function is in a continuous dimension, the maximum value can be attained by plugging in the already identified critical value which is 200 at the end point existing in the range as follows:P (0) = -80,000 P(200) = 240,000 P(250) = 220,000Therefore the above scenario indicates that the owner of the apartment may generate maximum profits if he rents out only 200 instead of all the 250 houses.

On the other hand, differentiation has also been used to perform various business activities in the contemporary society for example it has been widely used to calculate the maximum sizes of packaging materials with a few known dimensions while missing other important dimensions. A real example of the application of differentiation has been evident i.e. in a scenario where a sales person wants to determine the maximum size of a packaging box with a known length= x and known width= y, but without a known height.

This can be arrived at as:Volume= length. Width. Height also expressed as;V= l.w.h also;V (h)= (l-h). (w-h). h BibliographyThompson, H. E.2011. Applications of Calculus in Business and Economics. Menlo Park, Calif.: W.A. Benjamin.