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Cms 201: Operations Research I Question Paper
Cms 201: Operations Research I
Course:Bachelor Of Commerce
Institution: Kca University question papers
Exam Year:2009
1
UNIVERSITY EXAMINATIONS: 2008/2009
SECOND YEAR STAGE I EXAMINATION FOR THE DEGREE OF
BACHELOR OF COMMERCE
CMS 201: OPERATIONS RESEARCH I - SATURDAY
DATE: AUGUST 2009 TIME: 2 HOURS
INSTRUCTIONS: Answer question ONE and any other TWO questions
QUESTION ONE
a) Define Economic Order Quantity (EOQ) model and list any of its 5 assumptions [6 Marks]
b) Explain any 4 types of programming problems. In your explanation indicate the objective of
each problem, decision variable (s) and possible constraints [6 Marks]
c) Briefly explain any six areas of applicability of Operations Research [6 Marks]
d) At a Tool Service Centre the arrival rate is two per hour and the service potential is three per
hour. The hourly wage paid to the attendant at the service centre is Ksh.15 per hour and the
hourly cost of a machinist away from his work is Ksh.40.
i.) Calculate the average number of machinists being served or waiting to be
served at any given time [4 Marks]
ii.) Calculate the average time a machinist spends waiting for service [4 Marks]
e) Briefly explain the inventory control problem [4 Marks]
2
QUESTION TWO
Consider the project presented in table below:
Duration (in hours)
Activity Immediate Optimistic Most probable Pessimistic
Predecessor(s)
A - 4 6 8
B - 1 4.5 5
C A 3 3 3
D A 4 5 6
E A 0.5 1 1.5
F B,C 3 4 5
G B,C 1 1.5 5
H E,F 5 6 7
I E,F 2 5 48
J D,H 2.5 2.75 4.5
K G,I 3 5 7
a) Construct the network diagram for this project [6 Marks]
b) Identify the critical path and calculate the expected duration of the project [10 Marks]
c) What is the probability of the project being completed in one day (24 hours)? [4 Marks]
QUESTION THREE
A Tub manufacturing company manufactures types of tubs, Spa and Lux. A decision needs to be
made on how many of each type to produce. To produce each Spa 9 hours of labour and 12 feet of
tubing is required. Each Lux requires 6 hours of labour and 16 feet of tubing. The manufacturer is
equally aware that to produce each tub he will require one pump. In the next production cycle, only
200 pumps will be available. Also expected are 1566 production labour hours and 2880 feet of tubing.
The manufacture earns a profit of 350 on each Spa and 300 on each Lux sold.
a) State the decision variables [1 Mark]
b) State the objective function [2 Marks]
c) Determine the constraints [7 Marks]
d) Set up the LP model [3 Marks]
e) Use the graphical approach to find the optimal solution. Remove the graph paper attached to
this examination paper and use it to answer this question. [7 Marks]
3
QUESTION FOUR
With the help of an illustration, explain the following terms
a) An infeasible solution [3 Marks]
b) An unbounded solution
c) Redundant constraint [3 Marks]
d) A game [3 Marks]
e) Safety Stock [5 Marks]
f) Queue discipline [3 Marks]
QUESTION FIVE
A company manufacturing PC’s has to purchase components regularly from a supplier who offers the
following pricing regime:
Quantity Purchased Price per Component (in €)
< 500 5.00
500 – 999 4.90
1000 – 1999 4.80
= 2000 4.75
The company has an annual demand for 5000 of these components. Furthermore, it costs the company
€50 to place up an order (regardless of order size), and there is an inventory holding charge of 20% of
the value of the stock per annum.
a) Define the terms: Purchase cost, ordering cost and holding cost [6 Marks]
b) What order quantity will minimize the total annual cost [14 Marks]
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