CHAPTER ONE
INTRODUCTION
1.1. BACKGROUND OF THE STUDY: THE APPLICATION OF LINEAR PROGRAMMING IN PROFIT MAXIMIZATION (A CASE STUDY OF CRUNCHES FRIED CHICKEN AKA ROAD)
Linear programming (LP) can be defined as a mathematical technique for determining the best allocation of a firm’s limited resources to achieve optimum goal. It is also a mathematical technique used in Operation Research (OR) or Management Sciences to solve specific types of problems such as allocation, transportation and assignment problems that permits a choice or choices between alternative courses of action (Yahya, 2004). Linear programming is a term that covers a whole range of mathematical techniques that is aimed at optimizing performance in terms of combinations of resources (Lucey, 1996). Linear programming (LP) can be defined as a mathematical technique for determining the best allocation of a firm’s limited resources to achieve optimum goal. It is also a mathematical technique used in Operation Research (OR) or Management Sciences to solve specific types of problems such as allocation, transportation and assignment problems that permits a choice or choices between alternative courses of action (Yahya, 2004). Linear programming is a term that covers a whole range of mathematical techniques that is aimed at optimizing performance in terms of combinations of resources (Lucey, 1996).
The aim of every organization, company or firm is to make profit as that is what guarantees its continuous existence and productivity. Overtime, issues have been raised about the closure or liquidation of organizations, these chief amongst others may be as a result of lack of effective and sustainable profit maximization.
Businesses can only grow and expand when profit is made as profit is the major reason people go into business. In other to ensure economic development and generation of jobs, government and its stakeholders in the corporate world need to ensure that profit is being maximized as failure to do so would result to fatal economic and social consequences of retrenchment and economic under development. In the labour market, a lot have been done to ensure profit maximization in Nigeria, ranging from retrenchment of workers which is an anti-people approach to ensuring strict compliance to the mathematical or economic principles of profit maximization. The later, as good as it sounds have been elusive to companies and corporations, this has made companies and establishment to take the easy way out of lack of maximization of profit by retrenching of downsizing their workers. One of the mathematically proven ways to ensure profit maximization is the linear programming method.
Linear programming (LP) can be defined as a mathematical technique for determining the best allocation of a firm’s limited resources to achieve optimum goal. It is also a mathematical technique used in Operation Research (OR) or Management Sciences to solve specific types of problems such as allocation, transportation and assignment problems that permits a choice or choices between alternative courses of action (Yahya, 2004). Linear programming is a term that covers a whole range of mathematical techniques that is aimed at optimizing performance in terms of combinations of resources (Lucey, 1996).
Linear Programming being the most prominent OR technique, it is designed for models with linear objective and
constraint functions. A LP model can be designed and solved to determine the best course of action as in a product mix subject to the available constraints.
Generally, the objective function may be of maximization of profit (which is the focus of this paper) or minimization
of costs or labor hours. Moreover, the model also consists of certain structural constraints which are set of conditions
that the optimal solution should justify. Examples of the structural constraints include the raw material constraints, Production time constraint, and skilled labour constraints to mention a few. An optimum solution is a solution that fulfills both the constraints of the problem and the set objective to be met.
The term “linear”, as stated by Akingbade(1996), implies proportionality, which means that the elements in a
situation are so connected that they appear as straight line when graphed. While the “programming” indicates the
solution method which can be carried out by an iterative process in which a researcher advances from one solution to
better solution until a final solution is reached which cannot be improved upon. This finalsolution is termed the
optimal solution of the LP problem.
This work demonstrates the pragmatic use of linear programming methods in a manufacturing company in Nigeria
Linear Programming being the most prominent OR technique, it is designed for models with linear objective and constraint functions. A LP model can be designed and solved to determine the best course of action as in a product mix subject to the available constraints. Generally, the objective function may be of maximization of profit (which is the focus of this paper) or minimization of costs or labor hours. Moreover, the model also consists of certain structural constraints which are set of conditions that the optimal solution should justify. Examples of the structural constraints include the raw material constraints, production time constraint, and skilled labour constraints to mention a few. An optimum solution is a solution that fulfills both the constraints of the problem and the set objective to be met. The term “linear”, as stated by Akingbade (1996), implies proportionality, which means that the elements in a situation are so connected that they appear as straight line when graphed. While the “programming” indicates the solution method which can be carried out by an iterative process in which a researcher advances from one solution to better solution until a final solution is reached which cannot be improved upon. This final solution is termed the optimal solution of the LP problem. This work demonstrates the pragmatic use of linear programming methods in maximization of profit at the crunches fried chicken.
The aim of every organization, company or firm is to make profit as that is what guarantees its continuous existence and productivity. Overtime, issues have been raised about the closure or liquidation of organizations, these chief amongst others may be as a result of lack of effective and sustainable profit maximization.
1.2. STATEMENT OF THE GENERAL PROBLEM
The current alarming level of organizational liquidation which has led to the increase in unemployment or under employment has been a clog in the wheel of the economic advancement of the nation, the current high level of unemployment amongst our youths has led to the increase in social vices with youths resorting to other illegal means of livelihood, all these is actually as a result of the liquidation of companies and organizations who would have gainfully employed these youths an help in the contribution to the nation’s gross domestic products (GDP).
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