CHAPTER
ONE
INTRODUCTION
1.1. BACKGROUND OF THE STUDY
2. Linear programming (LP) can
be defined as a mathematical technique for determining the best allocation of a
firm’s
3. limited resources to
achieve optimum goal. It is also a mathematical technique used in Operation
Research (OR) or
4. Management Sciences to solve
specific types of problems such as allocation, transportation and assignment
problems
5. that permits a choice or
choices between alternative courses of action (Yahya, 2004). Linear programming
is a term
6. that covers
a whole range
of mathematical techniques
that is aimed
at optimizing performance
in terms of
7. combinations of resources
(Lucey, 1996).
8. Linear programming (LP) can
be defined as a mathematical technique for determining the best allocation of a
firm’s
9. limited resources to achieve
optimum goal. It is also a mathematical technique used in Operation Research
(OR) or
10.
Management Sciences to solve specific types of problems such as
allocation, transportation and assignment problems
11.
that permits a choice or choices between alternative courses of
action (Yahya, 2004). Linear programming is a term
12.
that covers a
whole range of
mathematical techniques that
is aimed at
optimizing performance in
terms of
13.
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
final solution 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).
1.3. OBJECTIVE OF THE STUDY
The main objective of this study is to examine
the application of linear programming in profit maximization. Other objectives
of the study include;
1.
To highlight the peculiarities of
using linear programming technique at the crunches fried chicken and prove that
despite the obstacles, the application of the technique in determining the
profit maximization in Crunches fried chicken would be more profitable than
otherwise.
2.
To encourage companies to adopt the
application of linear programming technique in ensuring maximization of profit.
It seeks to illustrate the profitability of using the technique despite the
peculiarities of applying it in the particular economic environment.
1.4. SIGNIFICANCE OF THE STUDY
The
finds from this study would be of immense importance to government
establishments, captains of industries and employers of labour as it would help
in them in profit maximization and organizational growth and expansion. This
study would equally benefit students, scholars and researchers who are
interested in the linear programming research.
1.5. RESEARCH METHODOLOGY
Crunches
fried chicken is chosen for this study for two main reasons. First, it uses the
trial-and-error method in arriving at major management decisions even when the
research department feels that a linear programming approach would have given a
better result. Secondly, Crunches fried chicken produces eight different
products which makes the determination of the quantity combinations of the
products produced an important and major management decision. The research is
designed to cover one month, 1st to 31st July, 2016. Researchers have
investigated the overall quantity combination of the eight products produced by
Crunches fried chicken, Uyo during the research period and the allocation of
resources to the various products. This has been made possible by the records
kept by the Production Line Manager and the Sales Department relating to the
different brands of products produced by the firm, the technical coefficients,
the raw materials available and their relative prices. Researchers also had
personal interview with a representative of the management. Researchers then
applied linear programming to determine a new quantity combination. The total
contribution to profit of each of the products for the month using the new
quantity will now be compared with the total profit contribution made by the
former product mix determined by the trial-and-error method. The problems
encountered in the process will be noted and from personal interviews and
relevant records, other peculiarities shall be established. When there are n
choice variables and m constraints, the linear programming takes the general
form with a linear objective function, a set of linear inequality constraints
and a set of non-negativity restrictions as its major ingredients. The
generalized n variable linear programme can be stated as below:
1.6. SCOPE OF THE STUDY
This
study would be restricted to the application of linear programming in profit
maximization using the crunches fried chicken uyo as a case study.
1.7.
LIMITATION OF THE STUDY
The
researcher was constraint by time as time frame for the submission of this
research was short for an expansive research.
The
researcher equally encountered financial limitation as lack of sponsorship from
corporate bodies thus; the researcher’s little resources could not cover more
areas.
1.8. DEFINITION OF TERMS
Linear programming:
a mathematical method of solving practical problems (as the allocation of
resources) by means of linear functions where the variables involved are
subject to constraints
Development:
the act or process of growing or causing something to grow or become larger or
more advanced
Profit Maximization:
A process that companies undergo to determine the
best output and price levels in order to maximize
its return. The company will usually adjust
influential factors such as production costs, sale prices,
and output levels as a way of reaching its profit goal.
There are two main profit maximization methods used, and they
are Marginal Cost-Marginal Revenue Method
and Total Cost-Total Revenue Method. Profit maximization is a good
thing for a company, but can be a bad thing for consumers if the
company starts to use cheaper products or decides to
raise prices.