kepong baru kl 2013 m3(q)

8/13/2019 KEPONG BARU KL 2013 M3(Q)

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CONFIDENTIAL*

STPM Trial 950/3

[Turn over*This question paper is CONFIDENTIAL until the examination is over.

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SMK KEPONG BARU KL

Section A [45 marks]

Answer allquestions in this section.

1 Eighteen months ago, Aini deposited RM 3000.00 in a savings account earning 5%

interest compounded semi-annually. At the same time, she deposited RM 150.00 at the end of

every month in another account earning 3% interest compounded monthly. Today, she

intends to withdraw all her money from both accounts to pay part of the 10% down payment

for a new car. The cash price of the car is RM 80000.00.

(a) Calculate the total withdrawal from both accounts. [5 marks]

(b) Aini plans to take up a loan from a finance company to finance the 90% balance

of the price of the car. The finance company charges interest at 4.5% compounded monthly

and the loan is payable in eight years. How much will the monthly payments be?

[4 marks]

2 (a) (i) What does consumers surplus measure? [1 mark]

(ii) Bobby is willing to pay up to RM 100.00 for a ticket to a concert, but

actually he pays RM 60.00. Calculate his consumers surplus. [1 mark]

(b) Suppose that the demand and supply functions are given as follows;

D= p+ 12

S= 2p+ 3

Find the equilibrium price. [2 marks]


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3 The table below shows the initial tableau of a particular linear programming problem

involving two variablesxandy.

P x y s t u v

1 -3 -5 0 0 0 0

0 1 1 1 0 0 10

0 1 2 0 1 0 14

0 3 2 0 0 1 18

State the three non-trivial inequalities inxandyand state the objective function. [4 marks]

4 A construction company is bidding on a contract to install a line of microwave towers.

It has identified the following activities, along with their duration, predecessor restrictions,

and work requirements, as shown in the table below.

Activity Preceding Activities Duration (Weeks) Crew Size (Workers)

A - 4 4

B - 7 2

C A 3 2

D A 3 4

E B 2 6

F B 2 3

G D, E 2 3

H F, G 3 4

(a) Draw an activity-on-arc network for the project. [3 marks]

(b) Construct a Gantt chart for the activities, and hence, draw a resource histogram.

[6 marks]

(c) Determine the minimum number of workers required to complete the project in

14 weeks. [3 marks]


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5 Suppose that the R & B Company has a soft drink product that shows a constant

annual demand rate of 3600 cases. A case of the soft drink costs RM 3.00. Ordering costs are

RM 20.00 per order and cost of holding is 25% of the value of the inventory. R & B

Company has 250 working days per year, and the lead time is 5 days.

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

(b) Determine the reorder point and the cycle time. [4 marks]

6 A town has only two banks, bank Rand bank C, and both compete about equally for

the towns business. Each week each bank decides on the use of one, and only one, of the

following means of promotion: TV, radio, newspaper, and mail. A marketing research firm

provided the following payoff table, which indicates the percentage of market gain or loss for

each choice of action by Rand by C (we assume that any gain by Ris a loss by C, and vice

versa ).

TV Radio Newspaper Mail

TV 0 -1 -1 0

Radio 1 2 -1 -1

Newspaper 0 -1 0 1

Mail -1 -1 -1 0

Use dominance argument to reduce the table to a 2 x 2 game. [2 marks]

Determine

(a) the dominated strategies, [2 marks]

(b) the optimum strategies for bankR and bank C, [4 marks]

(c) the value of the game, [1 mark]

(d) the expected value of the game forRif both banks always use the newspaper.

[1 mark]


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Section B [15 marks]

Answer any one question in this section.

7 A manufacturer of a new patented product has found that he can sell 70 units a week

direct to the customer if the price is RM 48.00. In error, the price was recently advertised at

RM 78.00 and, as a result, only 40 units were sold in a week. The manufacturers fixed costs

of production is RM 1710.00 a week and variable costs is RM 9.00 per unit.

(a) Show the equation of the demand function connecting price (P) to quantity

demanded (x) is P= 118x. [4 marks]

(b) Find the manufacturer break-even prices [5 marks]

(c) Recommend a unit price which would maximize profit, and find the profit

generated at that price. [6 marks]

8 A production line can be set up to produce either product X or product Y. The

following table gives the breakdown for each product.

Product Labour(minutes) Materials(kg) Testing minutes

X 30 2 3

Y 15 4 4

In any one week, only 30 hours of labour and 300 kg of material are available, and

owing to cost and availability, the testing equipment must be used for at least 4 hours. Also,

because of existing orders, at least 20 units ofXproduct must be produced. The contribution

from each unit of Xproduced is RM 12.00 and each unit of Y is RM 9.00. Using graphical

method, find

(a) the weekly production that minimises contribution and calculate this resulting

contribution.

(b) the percentage utilization of the available labour for minimum contribution.

[15 marks]

kepong baru kl 2013 m3(q)

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