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SEKOLAH MENENGAH KEBANGSAAN KEPONG

Section A [45 marks]Answer al l quest ions in this sect ion.

1. Johnson has purchased a delivery van to be used by his factory. The van is bought with adownpayment of 15 % which is RM 13 500 and a loan. The loan is amortised with 60 monthlypayments at an interest rate of 4 % compounded monthly. The depreciation rate of the van is

10% per year. Calculate;a) the amount of the monthly payment. [3]b) the total amount of interest paid in 60 months. [3]c) the book value of the van when the loan is paid off. [2]

2. The revenue function and cost function (in RM) for producing xunits of model A watches in acompany are given as R(x) = 700x -x2 and C(x) = 50 000 +x2.a) Find the break even quantities. [2]b) Using the marginal approach, find the number of units of watches that must be produced to

maximize profit. [3]c) Calculate the maximum profit in RM. Hence, sketch the graph of profit function. [4]

3. By using graphical method,determine the optimal solution of the Linear Programming :-Maximize z = x + 2ySubject to 3x + y 12

3x + 6y 272yx 6

x 0, y 0 [5]

4. A project has the following schedule.

Activity Preceedingactivity

Duration(in days)

A - 3B - 2

C A 1

D A 4

E D 2

F B,C 3

G B,C 1

H E,F 3

I G 4

a) Construct an AOA(activity on arc) network for the project. [3]

b) Identify the critical path. [2]c) Determine the completion time. [1]d) Prepare a table with a list of the activities with their earliest start times,latest start times and total

floats. [3]e) If two workers are available, can the project be completed in the minimum time required?

[3]

5. The annual demand of school bags is 100 000 units. To achieve minimum inventory cost, thecompany orders 1 414 units each time. The cost to place an order is RM 10 and the holding costis 5% of the unit price. Finda) the unit price. [3]b) the reorder point if the lead time is 2 days and the company operates 300 days per year.

[3]

8/13/2019 KEPONG SELANGOR 2013 M3(Q)

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6. A two- person zero- sum game is defined by the pay-off matrix

522

453

231

Explain that the game is stable. Is it a fair game? [5]

Section BAnswer any one quest ion in this sect ion.

7. A manufacturer is producing two kinds of food products, X and Y using three types of rawmaterials. Each ton of X is a mixture of 0.4 ton of material I and 0.6 ton of material III. A ton of Yis a mixture of 0.5 ton of material I, 0.2 ton of material II and 0.3 ton of material III. Afterdeducting relevant costs, the manufacturer makes RM 40 for every ton of food product X and RM30 for every ton of food product Y. The amount available for materials I, II and III are 20 tons, 5tons and 21 tons respectively.a) Formulate as a linear programming problem for the manufacturers production. [5]b) Write down the initial and second simplex tableau. [5]c) The final simplex tableau is

x y S1 S2 S3y 0 1

3

10

0

9

20

20

S2 0 0

3

2

1

9

4

1

x 1 0

3

5

0

9

25

25

0 0

3

100

0

9

400

1600

i) How many tons of each food product should be produced to maximize profit?Whatis the profit? [3]

ii) Are all the materials being used?Determine the quantity if theres any unusedmaterial. [2]

8. Evon and Farah play a zer0-sum game. The pay-off matrix of Evon is shown below.

Farah

F1 F2 F3

Evon

E1 -1 2 -2

E2 3 3 0E3 4 -2 1

a) Find the play safe strategy for Evon and Farah. Explain if the game has a saddle point. [4]b) Why F1 should not be Farahs strategy? [2]c) Use a graphical method to determine the optimal mixed- strategy of Evon and Farah. Explain

why the mixed-strategy is better than the pure strategy for both Evon and Farah. [9]