INTRODUCTION

Warisan RMN is a company that conduct business of selling computer

components. It was esblished in Januari 2008. This company offer for the community a

new brand of computer components that are good in quality and durable.

Warisan RMN has own mission which is to be the leading among the company

that also sells the computer components in year 2015. This mission set up the company to

work harder in order to achieve it mission.Besides, this company had set up some

objectives as progress markers along the way to goal achievement. First is to have a

successful company that is a leader in customer service and that has a loyal customer

following. Second is to get maximum profit from selling the computer components.Third

is to have a healthy competition among the manufacturer company.

Next one is about the Business Philosophy. This company has set the‘Customer

is always right’ is as the philosophy and whatever the customer comments or unsatisfied

about our services, we take that as the positive feedback and try to turn over a new leaf.

Then, Warisan RMN has set the targets to sell it products to every layer

ofcommunity because everyone using the computer in daily life to make worksand so on.

If capable, this company also wants to market the products to world market and be the

best among the manufacturer company and not just in Malaysia only.

Futhermore, this products always got positive feedback from the customer

and the growth for thisproducts always increase by time in line with technology

improvements. So, this golden opportunity should be wisely useby our company in order

to gain the maximum profit

TASK SPECIFICATION

This task is actually focus on several elements as the key to solve all the problems

asked. First, on task 1 it asked to find the relationship betweendemand, d, and the selling

price, s, of the computer component by plottingthe graph. Then, interpret the graph, make

discussion and write on a brief explanation on the relationship between the demand and

the selling price of the computer components manufactured by WarisanRMN. Second

one in task 1 is about express the yearly profit, P, in terms of the selling price, s and

make some comment about it. Next, to find out the maximum profit and the corres-

ponding selling price of computer componentsby using two or more methods like using

completing the square and differentiation. Lastly in task 1 is about to find out the number

of the computer components to bemanufactured by the Warisan RMN in order to gain

maximum profit from selling it product.

After finished in task 1, switch to task 2. Focus in task 2 is about loan.In year

2009, Warisan RMN made a profit of RM200 000 and intends to increase its production

in year 2010. So, as the manager of Warisan RMN, need to decide on the amount of loan

and the period of the loan to be taken for that purpose. Then, the first focus in task 2 is

about the calculation on the total amount of interest incurred for each of repayment

period and their corresponding amount of loan. Next focus in task 2 is about calculation

of the average interest rate per month from the loan. Tabulate the results and make some

comment about it. Then, make tabulation on the amount of yearly repayment for the loan

taken of repayment period up to 5 years from RM10 000 to RM100 000. Futhermore, this

focus also required to show that the annual payment for loan amount of RM10 000,RM15

000,RM20000 and so on in form of progression by observing the total amount payment

for 12 months. Fourth focus is about to find out the maximum amount of loan, in

multiples of RM5000 for the each choice of repayment period:1year, 2 years, 3 years, 4

years and 5 years. After that, need to find out the loan option should the Warisan RMN

take and make some elaboration for that reason. Lastly focus in task 2 is find out about

the amount of the reserve fund at the each month until 31st December 2010 by assuming

that the bank gives an annual interest of 2.5% for the Warisan RMN reserve fund of

RM50 000 in the bank.

CONJECTURE

Warisan RMN has own goal which is to gain highest profit by selling it products

to community. We aim to reach the target by reduce the cost of production the computer

components but maintain it quality. This is hard to do because so many risk needed to

handle it up. All this up depends on demand, if the demands higher our company can get

the maximum profit but if don’t our company will sick.

Then, our company need to have a strategic plan in order to get the maximum

profit by selling our product. There are many challenge outside because there are too

many company had manufactured the computer components, not just our companybut

only different onit brands.The customer must select the product that have good quality

and the cheapest one. We will try our best in our product in order to give satisfied to the

customer. Remember this slogan..’Customer is always right’ and we as the seller need

to give them the best services. If our products is good and best, customer must came

again next time and maybe with their friends. In this way, our company can reach for our

goal soon.

Besides, the demand for this products always increasing as fast as the technology

today. In t his modern life, everyone will use computer to make work because it is easy

and comfortable to use. So, if our company take this golden opportunity and fulfill the

demand of customer, just imagine how much that our company can gain from it selling.

Just be at the right time and place and then sell the product.

Here is the proposed solution for Part 1Part 1 (a)

Selling Price Per Unit, S, (RM) Estimated Yearly Demand, d, (units)

75 4500

125 3500

200 2000

250 1000

Demand of the computer decreases as its selling price increases. In other word, the higher the

100 150 200 25050

Selling price per unit

0

1000

2000

3000

4000

5000

Estimated Yearly Demand, d (unit)

selling price, the lower the quantity demand. In other hand, if the selling price per unit is

increased, the profit margin increased even the estimated yearly demand decreases. At same time,

if the selling price per unit is low, the profit margin is low but the estimated yearly demand is

high.Demanded products tend to be those that people must have, but they use only a fixed

quantity of it. Electricity is an example: if power companies lower the price of electricity,

consumers may be happy, but they probably won't use a lot more power in their homes, because

they don't need much more than they already use. However, demand for luxury goods, such as

restaurant meals, is extremely elastic - consumers quickly choose to stop going to restaurants if

prices go up.

If a company raises the price of a product, unit sales ordinarily falls. Because of this, pricing is a

delicate balancing act in which the benefits of higher revenues per unit are traded-off against the

lower volume that results from charging higher prices. The sensitivity of unit sales to changes in

prices is called the price elasticity of demand.

 A product's price elasticity should be a key element in setting its price. The price elasticity of

demand measures the degree to which the unit sales of a product or service are affected by a

change in price. Demand for a product is said to be inelastic if a change in price has little effect

on the number of units sold. The demand for designer perfumes sold by trained personnel at

cosmetic counters in department stores is relatively inelastic. Lowering prices on these luxury

goods has little effect on sales volume; factors other than price are more important in generating

sales. On the other hand, demand for a product is said to be elastic if a change in price has a

substantial effect on the volume of units sold. An example of a product whose demand is elastic

is gasoline. If a gas station raises its prices for gasoline, there will usually be a substantial drop in

volume as customers seek lower prices elsewhere.

Price elasticity is very important in determining prices. Managers should set higher markups over

cost where customers are relatively insensitive to price (i.e., demand is inelastic) and lower

markups where customers are relatively sensitive to price (i.e., demand is elastic). This principle

is followed in departmental stores. Merchandise sold in the bargain basement has a much lower

markup than merchandise sold elsewhere in the store because customers who shop in the bargain

basement are much more sensitive  to price i.e., demand is elastic.

Part 1 (b)Profit per unit of computer =

Total yearly profit,

Y =

Y = Total yearly profits = Selling Priced = demand

100 150 200 25050

Selling price per unit

0

1000

2000

3000

4000

5000

Estimated Yearly Demand, d (unit)

4500 – 1000

250 – 75

From the graph in Part 1 (a), we can see that there is a linear relationship the demand and the selling price. Therefore, we can use a straight line equation to represent this relationship.

First of all, let's find the gradient and the y-intercept of the graph.

Gradient

Then let's form the linear equation of the graph

Substitute this into the equation of yearly profit

Y = Y = Y =

Y =

Part 1 (c)Finding the maximum yearly profit

Method 1: By using calculus

Y =

Y is maximum when

Therefore, yearly profit Y is maximum when the selling price s = 175. This implies that when the selling price for the computer is RM175 per unit, the company will have the maximum profit potential.

Maximum Profit, Y =

Y = = RM 312 500

Method 2: Completing the squareWe can also find the maximum profit by using the completing the square method.

Y =

Y =

Y =

Y =

Y =

Maximum profit, Y = RM312,500 whens – 175 = 0s = 175

When the selling price s = RM175, the profit is maximum.

Part 1 (d)The number of computer,

d = −20s + 6000

For maximum profit, s = RM175

d = −20(175) + 6000d = 2500 unit.

The number of the computer components to be manufactured by the company in order to gain maximum profit,

d = 2,500 units

Part 2 (a)

Total amount of interest incurred for each choice of repayment period and their corresponding amount of loan is as follow:

Total Loan/RM

Total interest Incur12 Months 24 Months 36 Months 48 Months 60 Months

10000 2408 4808 7208 9632 12020

20000 4804 9616 14416 19216 24040

30000 7200 14400 21624 28800 36000

40000 9608 19208 28832 38432 48020

50000 12004 24016 36004 48016 60040

Part 2 (b)The average interest rate per month is as follow:

Total Loan/RM

Average Interest rate per Month12 Months 24 Months 36 Months 48 Months 60 Months

10000 2% 2% 2% 2% 2%

20000 2% 2% 2% 2% 2%

30000 2% 2% 2% 2% 2%

40000 2% 2% 2% 2% 2%

50000 2% 2% 2% 2% 2%

Since the interest rate is constant over time, hence the average interest per month remain the same every month. The average interest per month is also directly proportional to the amount of loan.

Part 2 (c)The amount of yearly repayment for each choice of repayment period up to 5 years for loan amounts from RM10 000 to RM100 000 is as follow:

Total Loan/RM

Annual Payment12 Months 24 Months 36 Months 48 Months 60 Months

10000 12408 7404 5736 4908 4404

15000 18600 11100 8604 7356 6600

20000 24804 14808 11472 9804 8808

25000 31008 18504 14340 12252 11004

30000 37200 22200 17208 14700 13200

35000 43404 25908 20076 17160 15408

40000 49608 29604 22944 19608 17604

45000 55800 33300 25800 22056 19800

50000 62004 37008 28668 24504 22008

55000 68196 40704 31536 26952 24204

60000 74376 44412 34404 29405 26412

65000 80604 48108 337272 31800 28608

70000 86808 51816 40140 34308 30812

75000 93000 55512 43008 36756 33012

80000 99204 59208 45864 39204 35208

85000 105395 62916 48732 41664 37416

90000 111600 66612 51600 44112 39612

95000 117804 70320 56184 46560 41820

100000 124008 74016 57336 49008 44016

For total annual payment for 12 months, the payment are

12408, 18600, 24804, 31008, 37200, 43404, 49608 .....

T2 − T1 = 18600 − 12400 = 6192T3 − T2 = 24804 − 18600 = 6204T4 − T3 = 31008 − 24804 = 6204T5 − T4 = 37200 − 31008 = 6192T6 −T5 = 43404 − 37200 = 6204T7 − T6 = 49608 − 43404 = 6204

We can see that, the difference of the annual payment is 6192 and 6204. The difference is approximately the same, hence we assume that the annual payment form an arithmetic progression with common difference.

Part 2 (d)(i)

The company allocated 20% of the profit made on loan repayment.

20% of profit = = RM 40000

From the table above, we find that, if the company allocate RM40,000 for loan repayment, the amount of loan it can take for repayment period, 1, 2, 3, 4, and 5 year are as follow:

Repayment Period (Year) Maximum Loan (RM)1 300002 500003 65000

4 80000

5 90000

Part 2 (e)

Monthly Interest =

The amount of the reserve fund at the end of each month until 31st December 2010 is as follow:

End of Month Amount of Reserved Fund

31/01/2010

28/02/2010

31/03/2010

30/04/2010

31/05/2010

30/06/2010

31/07/2010

31/08/2010

30/09/2010

31/10/2010

30/11/2010

31/12/2010

Further Exploration There are a lot of financial sources available in the market nowadays. We must be very particular and careful when we wan to choose the financial source.

Let we look at the Overdraft. An overdraft is a temporary facility added to bank accounts where you are able to be overdrawn in your bank account by a certain amount. You are charged interest based on the amount overdrawn and the length of time overdrawn, and are usually charged a regular fee for the use of the facility.

An overdraft is particularly useful when you have regular sales and purchases coming out of your account which could leave you in bad cashflow situations. They are a good backup to ensure you can pay your bills even when you have not yet received your invoice payments.

An overdraft is not supposed to be a permanent source of finance, and if your business is relying on using it, you should get your finances checked out.

Advantages of Overdrafts

Flexible – An overdraft is there when you need it, and costs nothing (apart from possibly a small fee) when you do not. It allows you to make essential payments whilst chasing up your own payments, and helps to maintain cashflow. You only need to borrow what you need at the time.

Quick – Overdrafts are easy and quick to arrange, providing a good cashflow backup with the minimum of fuss.

Disadvantages of Overdrafts

Cost – Overdrafts carry interest and fees; often at much higher rates than loans. This makes them very expensive for long term borrowing. You also face large charges if you go over the agreed overdraft limit.

Recall – Unless specified in the terms and conditions, the bank can recall the entire overdraft at any time. This may happen if you fail to make other payments, or if you have broken terms and conditions; though sometimes the banks simply change their policies.

Security – Overdrafts may need to be secured against your business assets, which put them at risk if you cannot meet repayments.

Choosing overdraft or not is depends on our situation and rely on the type of business. Now, we look at second type of financial sources, bank loan.

Using bank loans and overdrafts are two of the most common types of finance used by small businesses. Yet a surprising number of businesses are still failing to get the best deal from bank finance, and many are finding they could get a better deal through other forms of finance.

Here is a detailed look at bank loans and bank account overdrafts, helping you to decide whether they are the right kind of finance for your business.

Bank Loans

If you asked most new business people how they expect to get finance, the vast majority would say ‘a business loan from the bank’. The routine of new business owners going to the bank with their business plan in hand and trying to persuade the bank that the idea is a profitable one has changed very little over the past 30 years.

How Do Bank Loans Work? Bank loans work in much the same way as secured personal loans, the bank lends you money, with repayment over a set number of years at a particular interest rate.

The loans are usually secured against your house or other personal and business assets (e.g. Expensive machinery); so if you cannot pay them back your property will be at risk. Bank loans can range from a couple of thousand to many hundred thousands of pounds depending on the security and business prospects you can offer. You will be unlikely to get a loan of several hundred thousand pounds if you are opening a village corner shop.

The payment periods of bank loans vary considerably depending on the amount borrowed and the individual lenders terms and conditions. The typical loan periods are between 1 and 10 years, with some going up to 20 years, though each lender is likely to have a number of different loan packages to suit various business needs. The riskier your business, the less you are likely to able to borrow, and the higher the interest rate you will be asked to pay. This helps the bank to ensure that they are covered even if the risk does not pay off.

Remember that even if you are a limited company, your loan will probably still need to be secured on your home or other assets.

Advantages of Bank Loans

Reliability – Loans are very reliable and secure, you are assured the money for the duration of the loan (unless you break terms and conditions), and the odds of a bank or major lender requiring immediate pay back is tiny. You will also be fully aware of what you owe and your repayments (unless you choose a loan with a variable interest rate).

Cost – Compared to many other forms of finance, a bank loan is very reasonable in cost. Although loans are not cheap, they do not have the interest rates or charges of credit cards and overdrafts, and do not require you to give up a portion of your business as you would with investors.

Equipment Life – If you are using a loan to buy equipment, you may be able to tie the loan to the usable life of the product; saving you from having to pay out in one go for expensive machinery.

Disadvantages of Bank Loans

Inflexible – Once payment terms have been set you need to stick to them, and if you borrow more than you need you could end up paying lots of extra interest needlessly.

Security – If your loan is secured against your home or other assets, they will be at risk if you cannot afford to keep up repayments. Having the loan secured does provide lower interest rates,

but it does mean you need to be more careful about repayments; and also be very wary of borrowing more than you can afford to repay.

Charges – Most loans will have an arrangement fee when you first get the money, while many will charge you if you repay the loan before the end of the agreed period

We have just go thought all the advantage and disadvantage of the overdraft and bank loan, from that we can choose the best financial source suitable for our own business. Now we are going look at the difference between loans in the market now.

For the interest of the readers, the unique features of the conventional banking and Islamic banking are shown in terms of a box diagram as shown below:-

Conventional Banks Islamic Banks

1. The functions and operating modes of conventional banks are based on fully manmade principles.

1. The functions and operating modes of Islamic banks are based on the principles of Islamic Shariah.

2. The investor is assured of a predetermined rate of interest.

2. In contrast, it promotes risk sharing between provider of capital (investor) and the user of funds (entrepreneur).

3. It aims at maximizing profit without any restriction.

3. It also aims at maximizing profit but subject to Shariah restrictions.

4. It does not deal with Zakat. 4. In the modern Islamic banking system, it has become one of the service-oriented functions of the Islamic banks to be a Zakat Collection Centre and they also pay out their Zakat.

5. Lending money and getting it back with compounding interest is the fundamental function of the conventional banks.

5. Participation in partnership business is the fundamental function of the Islamic banks. So we have to understand our customer’s business very well.

6. It can charge additional money (penalty and compounded interest) in case of defaulters.

6. The Islamic banks have no provision to charge any extra money from the defaulters. Only small amount of compensation and these proceeds is given to charity. Rebates are give for early settlement at the Bank’s discretion.

7. Very often it results in the bank’s own interest becoming prominent. It makes no effort to ensure growth with equity.

7. It gives due importance to the public interest. Its ultimate aim is to ensure growth with equity.

8. For interest-based commercial banks, 8. For the Islamic banks, it must be based on a

borrowing from the money market is relatively easier.

Shariah approved underlying transaction.

9. Since income from the advances is fixed, it gives little importance to developing expertise in project appraisal and evaluations.

9. Since it shares profit and loss, the Islamic banks pay greater attention to developing project appraisal and evaluations.

10. The conventional banks give greater emphasis on credit-worthiness of the clients.

10. The Islamic banks, on the other hand, give greater emphasis on the viability of the projects.

11. The status of a conventional bank, in relation to its clients, is that of creditor and debtors.

11. The status of Islamic bank in relation to its clients is that of partners, investors and trader, buyer and seller.

12. A conventional bank has to guarantee all its deposits.

12. Islamic bank can only guarantee deposits for deposit account, which is based on the principle of al-wadiah, thus the depositors are guaranteed repayment of their funds, however if the account is based on the mudarabah concept, client have to share in a loss position..

 

CONCLUSION

After doing research,answering questions,drawing graphs and someproblem solving, I realise that the usage of additional mathematic isimportant in daily life. It is not just widely used in teaching but also at allevery aspect in life whether we realise or not. About this project, overallit quite interesting because I need to plan it carefully because it aboutfuture. It starts from making the relationship between the demand andthe selling price of the computer component followed by express theyearly profit in terms of selling price. Then find the maximum profit fromthe selling computer components and determine the number of theproducts to be manufactured by the company in order to gain maximumprofit.

Apart from that, in part 2 is all about loan. The rate of interest,repayment of the loan and which loan to be takenfor the company. It sogood because followed step by step. Then about further exploration isgood session because can open my mind about banking in Malaysia. Ialso got some new information that I never know before after doingsome research about other commercial loans or others financial sources.

Reflection

Additional Mathematics project 3 help me to learn and develop new skills and develop, assume responsibilities and providing a variety of enriching useful and practical experiences.

Before starting on this project, I was not good in a few topics, such as ‘Statistics’, and ‘differentiation’. But after completing this project work, I have improved in these topics. This project work really gave me a bright opportunity to master these topics. Besides that, I realized the importance of mastering these topics to enhance the application of it in our daily life.

I have also gained a lot of experience in presenting a paperwork through this project. I hope that in future, this experience will help me to present and submit my paperworks if I am to be the head of any projects in my profession. I have learnt the proper ways of giving concrete reasons for my choice too. I can think more rationally and wisely compared to before.

I have also learnt how to manage my time wisely as time is an essential part of life. As Shakespeare once said, “Time and the hour run through the roughest day”. All the time I spent on this project work has paid off and all the roughest time I went through is worth it all as my project work is complete.

Furthermore, this project work has given me a chance to develop a better communication with my teachers, parents and friends. I am glad that I could foster a strong relationship with everyone involving this project. I was also helped morally and financially by my friends and parents. Hence, I would like to thank all my parents and friends for their support. Finally, I would like to thank all my teachers for supporting me throughout this whole project. I would not have completed this assignment if it was not for my teachers. According to Josef Albers, "Good teaching is more a giving of right questions than a giving of right answers". And yes I have realized that this quote is true indeed. Thank you teachers.

Conclusively, I am very glad and satisfied that I have successfully completed this Additional Mathematics Project Work. This assignment has instilled a lot of moral values

and good knowledge in me. As the saying goes, “One of the greatest joys known to man is to take a flight into ignorance in search of knowledge.”

Contents

Introduction

Task Specification

Conjectures

Problem Solving : Part 1

Problem Solving : Part 2

Verification

Further Exploration

Conclusion

Reflection