SEKOLAH MENENGAH KEBANGSAAN BUKIT MERTAJAM

Section A [45 marks]

Answer all questions in this section.

1. Azman buys a van at RM 90000. Using the flat rate deprecation method and a depreciation

rate of 15% per year,

(a) determine the book value of the van at the end of 3 year, [2]

(b) find the number of years Azman will sell the van if he plans to sell the van when its

scraps value reaches RM9000. [2]

2. The cost function and revenue function in RM for a furniture company is given by

450003)( 2 xxC and xxR 750)( . The company produces x units of table daily. Find

(a) The break-even quantities. [2]

(b) Using the marginal approach, determine the number of units of table that must be

produced in order to maximize the profit. [3]

(c) Find the maximum profit in RM. [1]

3. A company manufactures three types of products A, B and C from two raw materials P and

Q. The amounts of the raw materials used are shown in the following table.

Raw material Amount (g) required per unit or product

A B C

P 5 2 1

Q 1 2 4

Profit per unit (RM) 10 12 12

Every day the raw materials available are at most 3 kg and 2 kg for P and Q respectively.

(a) Formulate the above problem as a linear problem to maximize the profit. [3]

(b) By using the simplex method, determine the quantity for each type of product that

should be produced in order to maximize the total profit, Hence, state the maximum

profit obtained. [7]

4. The following table shows the activities for a project and their preceding activities and

duration.

Activity Preceding activities Duration (weeks)

A - 2

B - 3

C - 6

D A 9

E B 5

F C 9

G B,D 5

H F 4

(a) Draw a network diagram for the project showing the earliest start time and the latest

start time for each activity. [5]

(b) Determine the critical path. [1]

(c) Find the minimum time required to complete the project. [1]

(d) Calculate the total float of each activity of the project. [1]

(f) If each activity requires one worker, determine the minimum number of workers

required if the project is to completed in minimum completion time. [3]

5. A company decides to operate with a backorder inventory policy for its product. The

company expects to sell 6000 units of an electronic component per year. The cost per unit is

RM30 and the ordering cost is RM90 per order. The holding cost of this product is RM2.50

per unit per year and the backorder cost is RM 3.50 per unit per year.. The lead time to

receive an order is 5 working day. The company operates 250 days per year.

(a) Find the optimum economic order quantity. [2]

(b) Determine the reorder point. [3]

(c) Calculate the minimum total annual inventory costs. [3]

6. A two-person zero-sum game for players A and B is represented by the pay-off matrix

421

653

321

(a) Show that the game has a stable solution. [3]

(b) State the value of the game. [1]

(c) Determine the optimal strategy for each player. [2]

Section B [15 marks]

Answer any one question in this section.

7. Two year ago, En. Lee deposited RM5000 in a saving account in Bank A at an annual

interest rate 10% compounded every six months. At the same time, he deposited RM 100 at

the end of every month in another account in Bank B at an annual interest rate 6%

compound monthly. Today, he intends to withdraw all his money from both accounts to pay

part of the 10% down payment for a new car. The price of the car is RM90000.

(a) Calculate the effective rate corresponding to a nominal interest rate 10% per year

compounded every six months. [2]

(b) Calculate the total withdraws from both accounts. [7]

(c) Find the additional amount to settle the down payment. [2]

(d) En. Lee plans to take up a loan from a finance company to settle the 90% balance of

the price of the car. The company charges 5% interest compounded monthly and the

loan is payable in 8 years. Find the monthly payment. [4]

8. The demand and supply functions for an item are 250)( xxDy and

103)( xxSy respectively, where x represents the number of item and y represents the

prices in RM.

(a) Find the market equilibrium point. [3]

(b) On the same graph, sketch the demand and supply curves and shade the consumer’s

and producer’s surplus regions. [4]

(c) Determine the consumer’s surplus and producer’s surplus. [8]

END OF QUESTION PAPER