Final Examination Semester 1 / Year 2008

Transcription

1 Southern College Kolej Selatan 南方学院 Final Examination Semester / Year 8 COURSE : UANTITATIVE METHOD AND DATA ANALYSIS COURSE CODE : MATH3 TIME : / HOURS DEPARTMENT : COMPUTER SCIENCE CLASS : IT7-B, IT7-A, IT6-C LECTURER : LOW FEE NGOO Student s ID : Bath No : Notes to andidates: ) The question paper onsists of 4 page and 4 questions. ) Answer all questions. 3) Return the question paper with your answer booklet.

2 . A publisher is printing a new book. This book may be either a hard over book or a paperbak. There is a RM4 profit on eah hard over and RM3 profit on eah paperbak. It takes 3 minutes to bind a hard overed book and minutes to bind a paperbak. The total available time for binding is 8 hours. Through experiene the publisher knows that he needs at least hard overed editions and not more than 6 paperbaks. Find the number of paperbaks and hard overed editions that must be printed in order to obtain the maximum profit. (5 marks). (a) The network for a small building projet is shown as Figure below, together with the time, in days, required to omplete eah task. 7 3 F A 7 C D 4 G 6 END B 3 E Figure You are required to list the possible paths through the network and the length of the path ( in days) in eah ase. Then, state the ritial path and the projet duration. ( marks) (b) Creative Builders have been awarded a ontrat to build an offie blok. The projet has been broken down into a number of ativities as Table below. The overheads on this projet are RM5 per month. Construt a network diagram for this projet and hene determine the minimum projet duration and its assoiated ost. (5 marks) Page of 4

3 Ativity Immediately Duration in months Total ost (RM ) preeding ativity A 8 B 75 C A 3 35 D A 7 7 E B 5 6 F C, D 9 55 G D 3 H D, E 4 9 I G, H 3 55 Table 3. (a) The eonomi order quantity (EO) is one of the oldest and most ommonly known inventory ontrol tehniques. It is relatively easy to use, but it does make a number of assumptions. State five assumptions usually made in EO alulation. ( marks) (b) ABC Eletronis supplies miroomputer iruitry to a ompany that inorporates miroproessors into refrigerators and other home applianes. One of the omponents has an annual demand of 5 units, and this is onstant throughout the year. Carrying ost is estimated to be $ per unit per year, and the ordering ost is $ per order. (i) How many units should be ordered eah time and order is plaed to minimize the ost? ( 4 marks) (ii) How many orders per year are needed with the optimal poliy? (iii) What is the average inventory if osts are minimized? (iv) If the ordering ost is not $, and ABC Eletronis has been ordering 5 units eah time an order is plaed. For this order poliy to be optimal, what would the ordering ost have to be? ( 5 marks) Page of 4

4 4. (a) State five harateristis of a simple queue. ( marks) (b) The Muthu Cobbler heel bar employs 3 operators who an on average eah repair the heels of 5 pairs of shoes an hour. If the average number of ustomers requiring servie is per hour, alulate (i) traffi intensity. (ii) Probability that of there being no units in the system (iii) the average time a ustomer is in the system. (iv) the average number of ustomers in the system (v) whether any time would be saved for ustomers if the three hannel system with a servie rate of 5 per hour was replaed by a single hannel system Page 3 of 4

5 LIST OF FORMULAE Average inventory level = EO = * = DC h o D TC = C + C h Traffi intensity Probability that of there being no units in the system Average time in the system Average number in the system Single hannel system ρ = ρ = W = P = ( ρ ) Multi hannel system ρ =!( +!( n= n= = ( p ) W!( P + n! L = ρ( ρ ) L = P + ρ!( n ( ρ ) Page 4 of 4