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Ees302: Operations Research 1 Question Paper
Ees302: Operations Research 1
Course:Bachelor Of Economics
Institution: Kenyatta University question papers
Exam Year:2012
KENYATTA UNIVERSITY
UNIVERSITY EXAMINATIONS 2011/2012
FIRST SEMESTER EXAMINATION FOR THE DEGREE OF BACHELOR OF
ECONOMICS, BACHELOR OF ECONOMICS AND STATISTICS,
BACHELOR OF ECONOMICS AND FINANCE AND BACHELOR
OF ARTS
EES 302:
OPERATIONS RESEARCH I
DATE: Thursday, 8th December, 2011
TIME: 4.30 p.m. – 6.30 p.m.
------------------------------------------------------------------------------------------------------------
INSTRUCTIONS
Answer Question One and any other two questions.
Question One (Compulsory)
Hi Dec produces two models of electronic gadgets that use resistors, capacitors and chips.
The following table summarises the data of the situation:-
Unit Resource Requirements
Maximum
Availability (units)
Resource
Model 1 Model 2
(units) (units)
Resistor
2
3
1200
Capacity
2 1
1000
Chips
0 4
800
Unit Profit($)
3 4
Page 1 of 4
a) Formulate the linear programming problem for the firm and solve for the optimal
solution using the simplex method.
(15 Marks)
b) Interpret the above solution as thoroughly as possible. Be sure to interpret the
shadow prices/marginal values for the resources.
(5 Marks)
c) Formulate the dual problem corresponding to the problem in (a) above. Using the
dual theorems, determine the optimal solution to the dual problem.
(10 Marks)
Question Two
Acem manufacturing company has a current transportation schedule, which has been
questioned by the Board as to whether or not it is optimal. The company has three
factories and five depots. The necessary data regarding costs in dollars, factory
capacities and depot requirements are given below:
Factories
Depot
Depots
1
2
3
Requirements
A
5.00
4.00
8.00
800
B
3.00
5.00
4.00
400
C
8.00
7.00
4.00
500
D
6.00
7.00
6.00
400
E
6.00
7.00
6.00
600
Factory
1100
900
700
Capacity
Given the data above, give suggestions to the board on the optimal transportation
schedule.
(20 Marks)
Question Three
Excel Industries has four subsidiary companies whose accounts are to be audited.
The company has short-listed five audit firms that can be assigned any of the audit tasks.
The table below shows the fees charged by the audit firms to audit the accounts of the
respective subsidiary companies.
Subsidiary companies
Audit firm
Mayfair
Agrotech
Metro
Davtech
(Sh. Million) (Sh. Million) (Sh. Million) (Sh. Million)
AB
5
10
16
10
CD
18
14
12
16
EF
10
13
14
12
GH
13
6
10
16
JK
14
11
8
13
Page 2 of 4
Required:
i)
The assignment Excel Industries would make to minimize the total cost of
auditing the subsidiary companies.
(15 Marks)
ii)
The audit firm which will not be assigned any task
(1 Mark)
iii)
The minimum cost of auditing the subsidiary companies
(4 Marks)
Question Four
a) Distinguish between CPM and PERT as techniques used in project planning.
(5 Marks)
b) The time estimates in days for each activity in a project are as follows:
Completion time
Activity
Optimistic (a) Most expected (m)
Pessimistic (b)
1 – 2
4
8
12
2 – 3
1
4
7
2 – 4
8
12
16
3 – 5
3
5
7
4 – 5
0
0
0
4 – 6
3
6
9
5 – 7
3
6
9
5 – 8
4
6
8
7 – 9
4
8
12
8 – 9
2
5
8
9 – 10
4
10
16
6 - 10
4
6
8
Using the above information:
i)
Draw the project network
(5 Marks)
ii)
Determine the expected time for each activity and hence the critical path
(8 Marks)
iii)
What is the expected completion time of the project?
(2 Marks)
Question Five
A testing laboratory has seven samples to test for some properties. Each test is in two
parts. Each sample is always subjected to test 1 first then test 2. The laboratory has only
one machine of the type required for each part of the test. The time in minutes it takes for
every sample in each test is given below:
Page 3 of 4
Sample
1
2
3
4
5
6
7
Test 1
2
7
10
5
6
4
8
Test 2
3
9
8
2
11
3
11
a) Determine the order in which the samples should be tested to minimize the total
elapsed time.
(15 Marks)
b) If a start up cost of Shs. 10,000 is required for each machine and the running cost
is estimated to be Shs. 20 per machine hour but Shs. 30 per idle machine hour,
estimate the total cost of production.
(5 Marks)
Page 4 of 4
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