MAASAI MARA UNIVERSITY
REGULAR UNIVERSITY EXAMINATIONS
2015/2016 ACADEMIC YEAR
FIRST YEAR SECOND SEMESTER
SCHOOL OF BUSINESS AND ECONOMICS
MASTER OF BUSINESS MANAGEMENT
COURSE CODE: MBM 813
COURSE TITLE: OPERATIONS RESEARCH
DATE: 4TH MAY 2016
TIME: 11.00AM-1.00PM
INSTRUCTIONS TO CANDIDATES
1. Answer Question ONE and any other THREE questions
This paper consists of 4 printed pages. Please turn over.
Question 1
i.
A university has advertised for adjunct faculty for four field courses
whose authentic teachers have gone on maternity leave. Six teachers
who had previously worked for the institution have applied for the
jobs. From the past engagement the said teachers had all been
engaged in all the field courses and took the following times on each:
subject
A B
1 24 43
2 32 39
teacher 3 39 34
4 43 44
5 44 34
7 39 48
C
32
39
32
27
37
39
D
34
42
29
34
39
45
The university pays per hour, Show the optimal allocation.
ii.
iii.
iv.
v.
(6 Marks)
Two competing firms have two strategies each. If the payoff for each
pair of strategy is shown by the table, determine the preferred
strategies.
Advertise Don’t advertise
FIRM B Advertise
6,5
7,2
Don’t advertise
4,7
5,3
(8 Marks)
Explain how a transportation problem is a special linear
programming problem and with the help of a n-source and mdestination problem, show objective and constraint functions
(6 Marks)
Explain the assumptions of classical economic order quantity model
and show the consequence of violating each.
(6 Marks)
A firm produces four types of drinks. Each must go through two
processes in different machines. If the times taken in each process is
shown by the table, obtain the optimal sequence and show the idle
time in each machine.
(6 Marks)
M1
M2
A B C D
3 2 4 3
1 4 2 6
QUESTION 2
(10 Marks)
A small scale holder specializing in selling pre packed porridge (P) and boiled
beans (B) to construction workers can make a profit of nine and nineteen
shilling on a unit of porridge and beans respectively. To be allowed access to
the premises, she must supply at least five and three units of porridge and
beans respectively. To keep both porridge and beans warm she spends one
shilling on the former and three shilling on the later though she can only
spend twelve shilling on warming. All her wares are not made on sight hence
must be carried on a cart which a maximum carrying capacity of 48 cubic
inches. If Porridge and beans take six and eight cubic inches of space
respectively and that all items are always sold find:
i. The optimal quantities of each the trade shouldtake to the market
ii. By how much the profit margins of each change without affecting the
current equilibrium
QUESTION 3
(10 Marks)
A trader has orders of a product amounting to 6400 units a year. To place a
single order he spends 400 shillings. Since the items are collected from his
premises, holding cost is estimated at 32% per unit/ year. If his supplier offer
three price regimes as follows, find the optimal quantity he should order:
quantity
0 ≤ Q1< 2000
2000 ≤Q2< 2600
2600 <Q3
price
11.5
11
10.5
QUESTION 4
(10 Marks)
A particular project can be divided into ten activities. Facts about the activities
are summarized in the following table (duration in weeks):
Activity
I.
II.
Immediate
predecessor
O N P
A
8 9 11
B
2 4 10
C
3 5 10
D
A
2 4 6
E
A, B
3 6 11
F
C
1 7 12
G
C
3 6 11
H
E, F
6 6 6
I
E, F
5 8 10
J
D, H
4 6 15
show the expected completion period for the project
What Is the probability of completing the project three weeks before
the anticipated completion time.
QUESTION 5
(10 Marks)
A factory can manufacture 5000 items per month to fulfill demand of 30000
units per year. Carrying cost is 0.4/unit/month. It costs 900 to set up
operations and 13/unit/year to cater for shortages since the firm accepts
order even when it is closed. When closed the factory employs 30 guards at a
cost of 300 per day. (All monies are in thousand Kenya shillings)
i.
ii.
Find the total security bill per year, if the factory only employs
external security when not under operation
The firm currently has a godown with a capacity 0f 50M3 , and
intends either to rent out excess space or to rent in case of need,
explain the storage decision it should make If each item occupies 6M3
of storage space.
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