QTE 407 Assignments
Quantitative Techniques
Instructions: All assignments are in
this document. Kindly check the due date for each of the four assignments
Assignment
One
Young Hu a roads
contract has been given a contract to re-carpet Ngong road. The project manager
has identified eight essential activities in this network. He has also listed
the activity as below.
|
Activity
|
Preceding
Activity
|
Time (in weeks)
|
||
|
Optimistic
|
Most likely
|
Pessimistic
|
||
|
A
|
-
|
2
|
3
|
4
|
|
B
|
-
|
5
|
5.5
|
9
|
|
C
|
-
|
6
|
7
|
8
|
|
D
|
A
|
4
|
8.5
|
10
|
|
E
|
C
|
1
|
3.5
|
9
|
|
F
|
B, E
|
1
|
3
|
5
|
|
G
|
C
|
8
|
9
|
16
|
|
H
|
F, G
|
1
|
3
|
5
|
Required
a) Calculate the expected time and the variance of each
activity (8 marks)
b) Illustrate the project by an arrow diagram (4 marks)
c) Identify the critical activities
(2 marks)
d) Calculate the free float of each activity (4 marks)
e) What is the probability that the project will take less than
30 weeks (2 marks)
Assignment Two
(a) Define the following terms as used in
Transportation and assignment models:
(i)
Degeneracy;
(ii)
A slack variable;
(iii)
Balanced transportation model
(6 marks)
(b) The table
below represent the demand, supply and transportation cost of a given product.
|
Source
|
D1
|
D2
|
D3
|
D4
|
D5
|
Supply
|
|
S1
|
10
|
12
|
2
|
3
|
4
|
50,000
|
|
S2
|
4
|
10
|
9
|
2
|
8
|
20,000
|
|
S3
|
9
|
15
|
3
|
12
|
1
|
35,000
|
|
Demand
|
25,000
|
15,000
|
25,000
|
30,000
|
10,000
|
|
(i)
Determine the initial
allocation for the above transportation problem.
(4 marks)
(ii)
Test the
allocation for optimality
(6 marks)
(iii)
Calculate the
minimum transportation cost (4 marks)
Assignment Three
(a) You have been
employed by a first growing supermarket that has no inventory control system in
place. You feel this is not right and stock control should be done
professionally. The managing director has given you a chance to meet. What are
the advantages of inventory control that you would give him? (6marks)
(b) The table has the
time taken by each machine to finish a particular job
|
|
Machine 1
|
Machine 2
|
Machine 3
|
Machine 4
|
Machine 5
|
|
Job 1
|
3
|
9
|
2
|
3
|
7
|
|
Job 2
|
6
|
1
|
5
|
6
|
6
|
|
Job 3
|
9
|
4
|
7
|
10
|
3
|
|
Job 4
|
2
|
5
|
4
|
2
|
1
|
|
Job 5
|
9
|
6
|
2
|
4
|
6
|
(i) Solve the following assignment problem to minimize machine time. (10 marks)
(ii) Calculate the least total number of hours that
the machines would take to complete the five jobs
(4 marks)
Assignment
Four
(a) Explain
five situations where the economic order quantity may not apply.(5 marks)
(b) A fueling station takes exactly 3
minutes to serve one vehicle. Vehicles arrive according to a Poisson process at
a rate of one every 5 minutes.
Required:
(i)
The
average time a vehicle must wait for service (2 marks)
(ii)
The average number of clients in the
system (2 marks)
(iii)
The
probability of having three vehicles in the system (2 marks)
(c)
Ken Metals produce three products, A, B and C. The products yield a
contribution of KES 800, 500 and 1000 respectively. The products use a machine
which has 400 hours capacity per month and each unit of the products uses 2, 3
and 1 hour of this machine respectively. There are only 150 units available of
special component per month and products A and C use one unit each. There are
200kgs of a special alloy, product A uses 2kgs, and product C uses 4kgs per
unit .There is an agreement with a trade union to produce no more than 50 units
of product B in the month. The company wishes to find out the production plan
which maximizes contribution,
i)
Write
a linear program for this problem
(4 marks)
ii)
The simplex solution of the above problem is
given below. Interpret it
(5 marks)
|
|
x
|
y
|
z
|
S1
|
S2
|
S3
|
S4
|
b
|
|
S1
|
-0.5
|
0
|
0
|
1
|
-1
|
-0.75
|
0
|
100
|
|
z
|
1
|
0
|
1
|
1
|
2
|
0
|
0
|
150
|
|
y
|
0.5
|
1
|
0
|
0
|
0
|
0.25
|
0
|
50
|
|
x
|
-0.5
|
0
|
0
|
0
|
0
|
-0.25
|
1
|
0
|
|
|
450
|
0
|
0
|
0
|
1000
|
125
|
0
|
175000
|
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