1.0 Introduction

Production planning is the basic life wire of every organization. An

organization which has much interest on the quality of its product must have a

good product planning. Further more for products planning to be effective

there are certain tools which are expected of a company to apply. One of the

basic tools is linear programming. Therefore it is of the interest of the

researcher to see the need for applicability of linear programming using

simplex method to ease products planning.

Based on assumption it is believed that such application can bring about

effectiveness in the production planning and thereby increasing the output of

products.

1.1 Background of the Study

The term operational research came into being during the Second World War

as a result of research on military operations during this war. However the

technique and model employed dated flack to earlier dates. During the war it

was apparent that a single professional or profession cannot provide realistic

solution for the logistic and tactical needs of the military. As a result many

professionals from different fields were engaged to deal with the logistics of

various military operations.

After the war. following the success recorded by this group attempts were

made at applying the same model and technique to civilian problems. A force

to reckon within the development or the postwar operational research was

George B. Dantzig He developed the linear programming problem and its

solution method known as the Simplex Method in 1947 (Sharma 2004).

1.2 Statement of the Problem

The goal of every organization is to see how it could put the available scarce

resource into optimal use. However. most organizations are composed of systems

that work interdependently to achieve the organization's set objectives.

The Nigerian Breweries is a manufacturing company. Like any entrepreneur. The

aim is to maximize profit and reduce cost. Some of the problems faced by the

company are:

i. This company is faced with the problem of power supply which is most of

the time erratic in Nigeria. So they have to resort to the use of private

power supply.

ii. The company also have problem of water supply which is an essential

component in their manufacturing process. Dysfunctional water supply

could mean periods of reduced or non-production.

iii. The company is also faced with problems of logistics; especially

transportation. With the non-motorable Nigerian roads and poor road

networks delivery of finished products to the end consumers acquisition

and supply or raw materials are compromised.

All of these problems contribute immensely to the cost of production. It is the

aim of this study to find ways of reducing cost and increasing profit.

1.3 Significance of the Study

The operational research remains an invaluable tool in the provision of optimal

solutions to problem(s) faced by many systems. In spite of these erstwhile

antecedents no work has been done on this area to the best of my knowledge. It

became important therefore that I bring to notice the relevance of this subject to

all and sundry. It is the aim of this work that the applicability of operational

research will be well illustrated to enhance its usefulness among system

operators.

Operational research is important in striking a balance between conflicting

objectives especially where there are many alternative course of action for the

decision maker. A single decision that is best for the whole organization is

called global optimum. One that is good for only a faction of the organization

is called suboptimum decision. Operational research attempt to find global

optimum by analyzing interrelationships among the several components

involved in the problem.

1.4 Aims and Objectives of the Study

i. This Research will be conducted to investigate and give the company an

idea on how to accurately allocate their scarce resources among competing

alternatives and be able to make optimum profit for different production

mix.

ii. The research is aimed at improving the production situation of the

company and also encourages the company to accept (increase/improve)

the production of the most profitable product(s).

iv. The findings and recommendations will not only assist the Nigerian

Breweries to improve their production but will help in cutting cost

and this will lead to an increment in profit making.

1.5 Scope of the Study

This project is concerned with optimization of the production mix in order to

obtain the mix that gives the maximum profit to the company. The parameters

involved in the linear programming model are assumed to be known with

certainty. Therefore where there is a change in any of the parameters the

optimality of the result obtained here could not be guaranteed.

1.6 Limitation of the Study

Due to lack of time and fund the research will be carried out only within the

organisation. The data to be collected will also be strict due to policies of the

organisation.

1.7 Definition of Terms used in Linear Programming Problem

In this section we are giving definition of some terms used when solving linear

programming problem using Simplex Method.

Optimization

Optimization is the determination of an optimal value

(maximization/minimization) of an objective function subject to a set of

constraints.

Linear Programming

Linear programming deals with the optimization (maximization/minimization) of

a function of variables known as objective function subject to a set of linear

equalities and/or inequalities known as constraints. The objective function may

be profit cost production capacity or any other measure of effectiveness which

is to be obtained in the best possible or optimal manner. The constraints may be

imposed by different sources such as market demands production processes and

equipment storage capacity raw material availability etc (Gupta and Hira 2002).

Simplex Method

Simplex method is an algorithm.

An algorithm is a process where a systematic procedure is repeated (iterated)

over and again until the desired result is obtained.

The interpretation of the dual problem also provides an economic interpretation

of what the simplex method does in the optimal problem. The goal of the

simplex method is to find how to use the available resources in the most

profitable feasible way. To obtain this goal we must reach a basic feasible

solution that satisfies all the requirements on profitable use of the resources.

(Hiller and Lieberman 2005).

Decision Variables

This refers to candidates (products service project etc) that are competing with

one another for sharing the given limited resources. These variables are usually

inter-related in terms of utilization of resources. (Kapoor and Kapoor).

Constraints

These are linear regressions which are expressed in mathematical form. The

limitation under which optimization is to be carried out (like production capacity

man-power machine etc) which are to b allocated among various competitive

activities. These constraints must be capable of being expressed as linear

equations or inequalities in terms of decision variables. The solution of a linear

programming model must satisfy these constraints. (Kapoor and Kapoor).

Objective Function

The objective function is a linear form that describes the effectiveness of the

model which was to be maximized as a mathematical relationship expressed in

terms of the decision variable. (Kapoor and Kapoor).

Optimum (Optimal) Solution

The basic feasible solution to linear programming problem is said to be optimal

solution if it give a maximal or minimal of the objective function.