8/13/2019 ST. MARY SABAH 2013 M3(Q).pdf

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SMK ST. MARY, SABAH

Section A [45 marks]

Answer all questions in this section.

1. (a) A saving scheme involves an initial investment of RM 1000 and an additional

RM 500 at the end of each year for the next five years. Calculate the receivable sum at theend of five years assuming that the annual rate of interest paid is 5 per cent. [4]

(b) What annual repayment at the end of each year will be required to repay a loan of

RM 25000 over 25 years if the annual rate of interest is 9%? [3]

2. A company uses components at the rate of 500 a month which are bought at the cost of

RM 1.20 each from the supplier. It costs RM 20 each time to place an order, regardless of the

quantity ordered. The total holding cost is made up of the capital cost of 10% per annum of

the value of stock plus RM 0.03 per item per annum for insurance plus RM 0.06 per item per

annum for storage plus 0.03 per item for deterioration.

(a) Determine the economic order quantity and the frequency of ordering. [5]

(b) Determine the total annual cost of the ordering policy. [3]

(c) If the lead time is half a month and demand can be assumed constant, what should

the reorder level? [2]

3. The table below shows a pay-off matrix for player A in a zero-sum game.

Player B

I II III

Player A

I 15 - 45 15

II -15 30 -30

III 30 15 -30

Determine the optimal mixed-strategy for each player. Then find the expected value ofthe game. [8]

4. (a) A company is selling luxury cars. The marginal cost to produce the cars is given

by C(x) = 0.2x + 4 thousand dollars where x is the number of cars produced. It has been

determined that producing 10 cars cost 717,000 dollars. Find the cost function in terms of x.

[4]

(b) The production cost for manufacturing leather shoes consists of a fixed cost of

RM39,900 and a variable cost of RM 25 per pair of shoes. Each pair of shoes sells for RM60.

(i) Find the total cost and total revenue as functions of the number of pairs of

shoes produced. [2](ii) Determine the break-even point for the profit function. [2]

5. The demand and supply equations for a product are given by p = 90 7.15 q and

p = 0.2q2+ 20 respectively, where p is the price in RM and q is the quantity.

(a) Find the equilibrium price. [3]

(b) Calculate the consumers surplus. [4]

6. Solve the following problem using the simplex method.

Maximize p = 10x + y

Subject to x 1

20x + y 100x 0, y 0. [5]

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Section B [15 marks]

Answer any one question in this section.

7. Draw a network (AON) for the project based on the precedence table below.

[3]

Activities Preceding activities Duration Support staff

A

B

C

D

E

F

G

-

-

A

A, B

A, B

C

C, D

2

3

3

4

5

6

3

1

2

1

1

2

2

1

(a) Determine the earliest start time and latest start time for each activity, identify the

critical path and the minimum project duration. [6]

(b) Construct a Gantt chart and a resource histogram for the project if all activitiesstart as early as possible. [6]

8. A factory produces two types of products, A and B. Each unit of product A requires 2

labour hours and 1 machine hour, whereas each unit of productB requires 2 labour hours and

4 machine hours. There are not more than 120 labour hours and not more than 96 machine

hours available in the factory each day. The factory also decided that the number of units of

productB produced each day should not be more than 60% of the total daily production of

both products A andB. The profit for each unit of A is RM120 and each unit of B is RM200.

The factory intends to maximize the total profit each day.

Formulate the problem as a linear programming problem. [6]

By using graphical method, determine the number of units of product A and product Bthat should be produced daily in order to maximize the total profit, and find the maximum

total daily profit. [9]