OPERATIONSS RESEARCH

8/2/2019 OPERATIONSS RESEARCH

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TOPIC: MAXIMIZATION OF THE TOTAL PROFIT OF WYLSON COMPANY

LTD

ABSTRACT

The paper is an operation research project which focuses on the

maximization of the total profit of Wylson Company limited. This paper

focus on an objective function with two decision variables (raw cocoa

powder and sugar fused cocoa powder) as against a number of

constraints was used in this study. To achieve the aim of the objective

function which seeks to maximize the total profit it is showed that a

certain amount of tons of raw cocoa powder should be product as

against sugar fused cocoa powder .

Keywords: Decision Variables, Objective function, Maximization,

constraints.

1.0 DEFINITION OF THE PROBLEM

Wylson Company limited is an Agro-processing company which produces two distinct products

namely Raw Cocoa Powder and Sugar Fused Cocoa Powder respectively. Dry Cocoa seeds are

used as raw material for the production of these goods. The management of the company

realized there was a lot of waste occurring at it production mill. The company decided to find

ways of reducing the cost by minimizing the waste, whiles maximizing its profit. The company

had a profit of GHC 300,000 for Raw Cocoa Powder and GHC360, 000 for Sugar Fused Cocoa

Powder.


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The Mills two products come off the production line at different time rate. The company

allocates forty (40) hours of production time per week for the production for its two products.

Form the information received from the plant we extracted our variables and constraints.

Information extracted is as follows;

Tons per hour: Raw Cocoa Powder - 200

Sugar Fused Cocoa Powder- 140

Different Profitability

Profit per Ton: Raw Cocoa Powder - 25 (GHC)

Sugar Fused Cocoa Powder - 30 (GHC)

Maximum in Tons (averagely)

Raw Cocoa Powder - 6000

Sugar Fused Cocoa Powder 4000

If XB for the number of tons brand of the Raw Cocoa powder to be produced.

Xc for the tons of Sugar Fused Cocoa powder.


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The total hours to produce all these tons of Cocoa powder is (hours to make a ton of Raw Cocoa

powder )Xb +(hours tomake a ton of Sugar Fused Cocoa Powder)Xc.

This number cannot exceed forty (40) hours available for the week.

CONSTRAINT

(

)XB + (

)Xc 40

Production Limit

0 XB 6000

0 Xc 4000

For total Hours, the profit must be (profit per ton of brand RCP)XB + ( profit per ton of FCP)XC

Objective is to maximize Profit

Maximize 25XB + 30XC

Subject to

(

)XB + (

)Xc 40

XB 0, XC 0


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2.0 DATA GATHERING FOR THE PROJECT

Data for the study of this project was gathered by the use of both qualitative and

quantitative methods. The sources of data was form both primary and secondary

sources. Primary sources includes questionnaire sent to the company to be

answered by various department i.e. accounting and production department to

provide us with the relevant data. Already prepared profit data by the accounting

department served as our source of secondary data. The data acquired was

interpreted by using software known as Mathematica8

FORMULATING A MATHEMATICAL MODEL

RCP (XB) FCP (XC) AVAILABILITY

NO. OF HOURS PER

TON

40

MAXIMUM TONS 6000 4000


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PROFIT PER TON 25 30

OBJECTIVE FUNCTION

MAX = 25XB + 30Xc

Subject to

(

)XB + (

)Xc 40

XB 6000

XC 4000

NON-NEGATIVETY CONSTRAINTS

XB 0, XC 0

3.0 DERIVING SOLUTION FROM THE MODEL

Computation of the procedure for deriving solution to the project from the

formulated model was done by the use of computer based software. The solution

given by the software is attached as an appendix in this report. The solution given


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provides us with the amount of tons of each product to produce in other to

maximize profit.

4.0 TESTING THE MODEL

From the solution given by the computer based software we text the model to

find the point at which a higher maximization of the total profit of the company

can be attained. Below is a figure to show the highest feasible point.

5.0 PREPARING TO APPLY THE MODEL

It can be deducted from the solution provided that this project has been able to

use linear programming to scientifically design a model to ensure how profit can

be maximize at Wylson Agro-processing company. With the development of this


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model it is intended that the company uses it to help maximize profit. The

management sort to apply this model in their activities as been developed by the

team. The system includes the model solution and procedure (post optimality

analyses), and its operational procedures and implementation. The system can be

called on at regular interval to provide the specific numerical solution need if

there arises the need for some changes to be done. This report has generate an

insight for management to help them make some managerial decision for the

production of the two product by their company to achieve profit maximization

6.0 IMPLEMNETATION

Having developed a system that would help to maximize profit of Wylson

Company limited. The next phrase and the most important is to implement the

findings that the model provided. This stage is very critical because is at this stage


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that the success or failure of this model can be tested practically. The team has

resolved to be part of the implementation stage to enable them to ensure

whether the model has been implemented well and also can monitor to see if

there are any forms of flaws associated with it so they can deal with it. From the

analysis or solution produce by the computer base software in other for Wylson

Company limited to achieve profit maximization, the company will have to

produce 25,330.3 tons of raw cocoa powder product and 168.869 tons of sugar

fused cocoa powder product respectively.

In addition to this, it must be emphasized that the success of this stage that is the

implementation phase depends greatly on the support of both the top

management and the operating management. The following steps are what this

team seeks to follow in this phase are;

Give a detail explanation of the system to the operating management andits relationship to its activities.

Responsibility for developing procedures for the implementation of thissystem

A clear understanding and view will be given to employees at theproduction unit to know what is expected of them.


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The team will monitor the system to see whether there are any flaws andmodification made if possible.

7.0 SUMMARY

At Wylson Company limited the management realized there is a lot of

waste occurring at it production Mill for it products that is Raw cocoa

powder and Sugar fuse cocoa powder. The OR team had an object of

maximizing the total profit of the company by reducing the amount of

waste caused. Data and information for this project was gathered

through already prepared production data from the production

department, profit data prepared by the accounting department and

also through the administering of questionnaires. The data obtain was

use to construct or formulate a mathematical model for the problem. A

solution was derived from this model by using computer based

software Mathematica8. The model was tested to see which area in

the feasible region gives us the highest number of value and that

happened at a point 25330.3 on the x-axis, 168.869 on the y-axis given


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as a total profit of GHC 638,320. The information obtain was

communicated to the company for it implementation. This model is

being implemented at the company mills so as to maximize the total

profit of the company.

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