THE APPLICATION OF LINEAR PROGRAMMING IN PROFIT MAXIMIZATION
- Project Research
- 1-5 Chapters
- Quantitative
- Abstract : Available
- Table of Content: Available
- Reference Style: APA
- Recommended for : Student Researchers
- NGN 3000
Background of the study
Every company or organization in the world strives to find the most efficient method to run their operations so that they may maximize their profits despite the limited resources at their disposal (Oyekan et al., 2019). Planning and care for optimal production are consequently essential in order to maintain optimal profit making and the survival of such an organization (Kumar et al., 2013 & Rama et al., 2017). Considering the fact that resources in the real world such as material, money, manpower, space, and time are limited, production planning in this context refers to the process of putting various activities and measures into place in order to ensure optimal production that satisfies customers' demands (Kumar et al., 2018; Lokhande et al., 2017; Shaheen et al., 2015 & Sumathi, 2016). Every business has a selection of product lines, which together make up the assortment of goods and services that the firm offers to consumers. Determining the product mix of a certain firm is highly significant because it enables that company to concentrate its production efforts on those goods that are most relevant to increasing profits (Oyekan et al., 2019). In spite of this, a business may feel compelled to expand its product offerings in the hope of drawing in a larger number of clients, exposing itself to the possibility of selling items to its clientele that are of interest to just a subset of the total population of its clients. Taking into account the fact that different products call for varying quantities of production resources and generate varying amounts of expenses and revenues at various stages of production, there is a necessity for a mathematical method that can determine the product mix that will result in the highest overall profit (Rama et al., 2017 & Sumathi, 2016). This method of solving mathematical problems is known as the "Linear Programming (LP) paradigm." Linear programming, often known as linear optimization, is a method for maximizing the value of a linear objective function while adhering to linear inequality constraints and, in certain cases, linear equality requirements (Ammar et al., 2020; Kumar et al., 2018 & Oyekan et al., 2019). It is a method of operational research that is used to distribute a company's limited production resources in the most effective manner possible (Akpan et al., 2016; Kumar et al., 2018 & Shaheen et al., 2015). Since of this, the creation of a model is required, which is a highly critical step because the model must accurately represent a real-life scenario or system in order to facilitate accurate decision analysis (Ammar et al., 2020; Kumar et al., 2018 & Kumar et al., 2018). The majority of the time, production mix issues get complex when there are roughly five (5) or more items from the same department involved. This makes finding an algebraic solution tough and laborious. The simplex method (tableau), which employs iterative processes in the resolution of linear programming issues, is a technique that may be applied to the resolution of any significant issue of this kind (Oyekan et al., 2019). The human solution of a linear programming model using the simplex approach can be time-consuming and laborious, but the solution can be automated using a computer (using TORA software or any other software that is capable of managing LP) to be both quicker and more accurate.
1.2 Statement of the problem
The LP model was used by Rama et al., (2017) to schedule drivers in a transport co-operation. The goal was to identify the lowest number of drivers required for each shift in a day in order to decrease the amount of money spent on reserved drivers. A linear programming model was recognized by Woubante (2017) as a necessary quantitative decision making tool for the appropriate optimization of product mix in the garment sector. Alternative approaches to solving linear programming problems, such as the large M technique and the dual simplex method, which Lokhande et al., (2017) adopted, can cut down on the total number of iterations needed and save significant amounts of time. The simplex method of linear programming was utilized by Akpan et al., (2016) in order to determine the best distribution of raw materials for the manufacture of various loaf sizes of bread in a bakery sector. Sumathi, (2016) made the discovery that intercept values might be utilized to determine the equality requirements among the inequality constraints in order to create optimum solutions while addressing linear programming problems (Sumathi, 2016). The simplex approach of linear programming was utilized by Oyekan et al. (2019) in order to identify which size of bread contributed the most to the overall profit maximization of the organization. A sensitivity analysis was also conducted in order to find the least and maximum cost coefficients of the bread sizes that could be maintained inside the firm while still achieving the highest possible profit (Oyekan et al., 2019).
Due to the finite nature of resources, it is of interest in every optimization problem not only to obtain an optimal solution to the problem but also to find out how stable that optimal solution would be in the event that either the cost coefficient of the objective function or the right hand side resource constraint was altered. This is because it is always of interest not only to obtain an optimal solution of the problem but also to find out how stable that optimal solution would be. In light of this, a sensitivity analysis is performed in order to determine the quantities of the variables (the company's products) that would give the optimal solution, the range of values of such variables within which the optimal solution should not deteriorate, and also the shadow price, also known as the dual price, which is the price for acquiring an additional unit of each resource (in the event that the company runs short of any) for optimal production. This is done in order to determine the quantities of the variables that would give the optimal solution.
1.3 Objective of the study
The primary objective of this study is to evaluate the application of linear programming in profit maximization. Specifically, this study seeks to:
- determine how the limited resources (raw materials) of Nigeria Bottling Company could be allocated in order to maximize profit.
- determine the product(s) that contribute(s) maximally to such profit in Nigeria Bottling Company.
1.4 Research Questions
The following research questions are answered in this study:
- determine how the limited resources (raw materials) of Nigeria Bottling Company could be allocated in order to maximize profit.
- determine the product(s) that contribute(s) maximally to such profit in Nigeria Bottling Company.
1.5 Significance of the study
This study will be of immense benefit to manufacturing companies because it will expose then to the need of leveraging on the product(s) that contribute(s) maximally to profit in their organization. Also, this study will add to existing literature on this topic and shall serve as a reference piece to students, scholars and researchers who may wish to carryout further studies on this topic or related domain in the future.
1.6 Scope of the study
The data on which this is based are quantities of raw materials available in stock, cost and selling prices and also the profits from crates of each product. The profit constitutes the objective function while raw materials available in stock are used as constraints. This study is therefore delimited to manufacturing companies, hence, Nigeria Bottling Company is sampled in this study.
1.7 Definition of terms
Linear Programming: Linear programming is a mathematical modeling technique in which a linear function is maximized or minimized when subjected to various constraints.
Profit Maximization: Profit maximization is a process business firms undergo to ensure the best output and price levels are achieved in order to maximize its returns.
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