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Operations Research 1 Question Paper

Operations Research 1

Course:Bachelor Of Commerce

Institution: Kca University question papers

Exam Year:2011

UNIVERSITY EXAMINATIONS: 2010/2011
SECOND YEAR EXAMINATION FOR THE BACHELOR OF COMMERCE
CMS 201 OPERATIONS RESEARCH 1
DATE: DECEMBER 2011 TIME: 2HOURS
INSTRUCTIONS: Attempt question ONE and any other TWO question
QUESTION ONE
(a) How would you deal with the assignment problems where
(i)Some assignments are prohibited [2 marks]
(ii)The objective function is of maximization type [2marks]
(iii)Unbalanced problem [2 marks]
(b) A departmental store has a single cashier. During the rush hours, customers arrive at the
rate of 20 customers per hour. The average number of customers that can be processed by
the cashier is 24 per hour. Assume that the conditions for the use of single channel queuing
model apply .What is
i. The probability that the cashier is idle? [ 2marks]
ii. Average number of customers in the queuing system? [2 marks]
iii. Average time a customer spends in the system? [2 marks]
iv. Average number customers in the queue? [2 marks]
v. Average time customers in the queue? [2marks]
vi. Average time a customer spends in the queue waiting for service? [2 marks]
(c) Food A Contains 20 units of vitamin X and 40 units of Vitamin Y per gram.Food B
contains 30 units each of vitamin X and Y. The daily minimum requirements of vitamin X
and Y are 900 and 1200 units respectively.
Required
How many grams of each type of food should be consumed so as to minimize the cost, if
food A costs sh 60 per gram and food B costs sh 80 per gram. [12 marks]
QUESTION TWO
(a) Explain the following terms as applied in competitive situations:
i) Surplus variable [2 marks]
ii) Slack variable [2 marks]
iii) Artificial variable [2 marks]
iv) Unbalanced transportation problem [2 marks]
(b) Best Sell Ltd. has decided to launch a new product in addition to its range of products. The
following information is available:
1. The new product may be distributed through any combination of the two company
warehouses W1 and W2.
2. The available monthly production capabilities for the new products are:
1000 units at plant A
2000 units at plant B
1000 units at plant C
3. Three major concentration points of customer demand are at locations E, F and G
which are estimated to have a monthly demand of:
900 units at E
800 units at F
900 units at G
4. The unit production costs amount to Sh.30, Sh.40, Sh.10 at A, B and C respectively.
5. The unit handling costs at the warehouses amount to Sh.20 and Sh.30 at W1 and W2.
6. The unit transportation costs from plant to warehouse and unit delivery cost from
warehouse to customers are as shown below:
Determine the optimum production and distribution schedule to minimize total cost.
[12 Mark]
[Total: 20 Marks]
QUESTION THREE
Mwamba Development Group (MDG) plans to undertake a project consisting of eleven (11) tasks.
The expected completion time of each task is uncertain and this makes the project completion time uncertain. MDG has approached a consultancy firm for advice on the expected project completion time.
The consultancy firm intends to use simulation analysis to deal with the uncertainty of the project completion time. The following data were obtained by the consultancy firm, for the purpose of simulation analysis:
Activity Immediate
Predecessor
Duration in days and probabilities
Duration in days
Required:
(a) Explain the basic steps that can be used to solve this type of problem simulation
technique. [6 marks]
(b) Draw the network for the project and determine the critical path of the project. Use the
activity’s expected time to determine the expected completion time of the project.
[4 marks]
(c) Carry out four simulation runs for each activity and using the results of the simulation,
determine the expected project completion time. [6 marks]
(d) State two advantages and two disadvantages of the simulation technique. [4 marks]
Use the following random numbers.
95, 30, 59, 93, 28, 72, 09, 54, 66, 95, 36, 98, 56, 23, 60, 79, 14, 50, 61, 81, 84, 14, 24, 75,
85, 49, 05, 09, 53, 45, 60, 98, 90, 86, 74, 55, 69, 09, 10, 96, 40, 27, 15, 83
[Total: 20 marks]
QUESTION FOUR
Marashi Company Ltd. is a merchandising company selling a 40ml bottle of perfume in four zones
within Kenya. The variable cost per bottle is Sh.70 but the selling price is different in each of the
four zones. The difference in the selling price is due to the transportation costs involved. The
company has four salesmen available for an assignment in the four zones. The zones are not
equally good in their sales potential. It is estimated that a typical salesman operating in each zone
would bring the following annual sales:
Zone Mt.Kenya Western Nyanza Eastern
Annual sales in bottles
Selling price per bottle
60,000
100
50,000
110
40,000
130
30,000
120
The four salesmen also differ in their marketing ability. It is estimated that, working under the
same conditions, the yearly sales would be proportionately shared as follows:
Salesman: Kariuki Wafula Oketch Wambua
Proportion: 6 5 5 4
The objective of Marashi Company Ltd. is to maximize contribution from each zone.
Required:
(a) Determine how the four salesmen can be assigned to the zones in order for the company to maximize the total contribution. [15 mark]
(b) Calculate the total contribution of the company after the assignment. [5 marks]
[Total: 20 marks]
QUESTION FIVE
Peter Oloo is a fishmonger in Kisumu. As a result of adverse business changes in the region, the
supply and demand for fish are subject to random variations making it difficult to project the next day’s business.
Management accounts in relation to the previous 300 days reveal the following mode of behaviour:
Number of fish
purchased from
fishermen
Number of
days
Number of fish
Sold to
customers
Number of days
100 30 100 45
200 60 200 60
300 90 300 90
400 90 400 75
500 30 500 30
300 300
Peter Oloo buys each fish at Sh.40 and sells it for Sh.60 if sold on the same day; if the fish is sold the following day it will fetch only Sh.20. If not sold during the second day its value drops to zero and Peter Oloo donates it to children’s home. Peter Oloo’s Policy is to satisfy the days demand from the fresh fish first; and any further demand will be satisfied from the stock of fish from previous day. Failure to satisfy demand costs Peter Oloo Sh.20 for every fish supplied to the customer. There are no backorders in the business.
Required:
a) Simulate Peter Oloo’s operations for 8 days clearly indicating profits made each day.
[16 marks]
b) What are the average daily profits for Peter Oloo?
Use the following random numbers
573423709751483681320931644925928345 [4 marks]
[Total: 20 marks]

Operations Research 1 Question Paper

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