Abstract
Advertisement involves significant amount of money and remain as one of the major issues bothering companies and other investment sectors. Advertising is a marketing strategy directed to the consumers through any media in order to present and promote product, services and any other cause. Sale of products occurs with or without advertisement and may increase or decrease depending on the market situation. The question is, is there a mathematical model that can surely confirm the effects of advertising on sales of products? The aim of this paper is to develop a first order linear differential equation model that seeks to justify the impacts of advertising on the sale of products in Ghanaian market. Two basic variables, the advertisement and sales of product were considered for the model. A system of two differential equations from the two basic variables were developed and converted to first order non-homogeneous linear differential equation. The geometrical method was employed to obtain qualitative information about the solution of the first order non-homogeneous linear differential equation. The MATLAB software package was used to plots the graphs to illustrate the behaviour of the sale of products with respect to the time of advertisement. The findings revealed that differential equation model can be used to justify the advertising impacts on the sale of products.
Highlights
Though sales of products are influence by some variables such as growth of population, price changes and retail availability, it is believed that about eighty percent of the sales of products are influence by Advertisement
The alarming rate at which businesses and other investment sectors are advertising their products in the media has made the effect of advertisement on the sales of product so crucial that many researchers have started working in that area
The paper provided mathematical evidence to support the claim that advertisement has greater effects on the sale of products in the business environment. It further showed with graphs how well the model performed in analysing the impacts of advertisement on sale of products
Summary
Though sales of products are influence by some variables such as growth of population, price changes and retail availability, it is believed that about eighty percent of the sales of products are influence by Advertisement. Or indirectly advertisement has become part of the modern businesses and one cannot deal away with it It is one of the prudent ways employed by companies and other investment sectors to generate enough sales from their products. It doesn’t matter the approach one choses to organize advertisement to increase sales, there is the need to put in place well developed strategy to win consumers admiration or purchasing behaviour. Since the non-homogeneous first order linear differential equation model developed in this research cannot be solved directly, a new approach which leads to a qualitative understanding of the behaviour of solutions is employed. American Journal of Applied Mathematics 2020; 8(4): 171-175 order linear differential equation which virtually relates the advertisement of the product A(t ) to the sales of the product S (t )
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