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Dplm 0122: Operations Research Question Paper
Dplm 0122: Operations Research
Course:Diploma In Business Management
Institution: Chuka University question papers
Exam Year:2013
CHUKA
UNIVERSITY
UNIVERSITY EXAMINATIONS
FIRST YEAR EXAMINATION FOR THE AWARD OF
DIPLOMA IN BUSINESS MANAGEMENT
DPLM 0122: OPERATIONS RESEARCH
STREAMS: DPLM Y1S2 TIME: 2 HOURS
DAY/DATE: FRIDAY 9/8/2013 11.30 AM- 1.30 PM
INSTRUCTIONS:
Answer Question ONE and any other TWO
Show all our Workings Clearly
QUESTION ONE (30 MARKS)
1. (a) Give three definitions of operations research. [3 Marks]
(b) A firm has analysed their operating conditions, prices and costs and have developed the following functions revenue R=400Q-?4Q?^2 and cost
C=Q^2+10Q+30. Where Q is the number of units sold. The firm wishes to maximize the profits.
Required:
(i) Find what quantity should be sold. [4 Marks]
(ii) At what price. [2 Marks]
(iii) What will be the amount of profit? [3 Marks]
(c) State five basic assumptions of linear programming. [5 Marks]
(d) State and explain 3 major types of inventory. [3 Marks]
(e) The following data relate to a particular stock item,
Normal usage 110 per day
Minimum usage 50 per day
Maximum usage 140 per day
Lead time 25 – 30 days
EOQ (previously calculated) = 5000
Required:
Using the above data calculate the following control levels.
(i) Re-order level [3 Marks]
(ii) Minimum level [3 Marks]
(iii) Maximum level [4 Marks]
QUESTION TWO (20 MARKS)
(a) Customers at Jatomy supermarket arrive at the rate of 8 per hour. The service rate is 10 customers per hour.
Required:
(i) Calculate the traffic intensity [2 Marks]
(ii) What is the average No. of customers waiting for service? [2 Marks]
(iii) What is the average time a customer must wait in the queue? [2 Marks]
(iv) What is the average time for a customer to be in the system? [2 Marks]
(b) Use simplex method to maximize Z=?2X?_1+2X_2+X_3
Subject to ?2X?_1+X_2+?2X?_3=14
?2X?_1+?4X?_2+X_3=26
X_1+?2X?_2+?3X?_3=28
X_1=0,X_2=0,X_3=0. [12 Marks]
QUESTION THREE (20 MARKS)
(a) Use graphical method minimize Z=40X_1+?240X?_2
Subject to: ?20X?_1+?50X?_2=480
?80X?_1+?50X?_2=720
X_1,X_2=0 [8 Marks]
(b) The revenue function is given by 100q-q^2 and the total cost function by 40q+800
Required:
(i) Find the profit function. [2 Marks]
(ii) Find the level of output q that maximizes the profit function. [2 Marks]
(iii) What is the maximum profit? [2 Marks]
(c) Give 6 objectives of inventory control. [6 Marks]
QUESTION FOUR (20 MARKS)
Given the linear programming problem maximize ?3X?_1+?4X?_2
Subject to: A. ?4X?_1+?6X?_2=100 Machine hours
B. ?4X?_1+?6X?_2=180 Labour hours
C. X_1+X_2=40 Materials
D. X_(1 )= 20 Sales
E. ? X?_2=10 Sales
Where X_1= Units of Klunk
? X?_2= Units of Klick
Required:
(a) Find the shadow prices using the arithmetic method of binding constraints. [10 Marks]
(b) Find the shadow prices using dual formation method. [10 Marks]
QUESTION FIVE (20 MARKS)
(a) Explain 5 factors for the slow implementation of operations research. [10 Marks]
(b) A company uses 50,000 widgets per annum which cost £ 10 each to purchase. The ordering cost and holding cost are £150 per order and 15% of the purchase price per a widget stock respectively.
Required:
(i) Calculate EOQ [5 Marks]
(ii) Assuming that the firm described above has decided to make the widgets in its won factory. The necessary machinery has been purchased which has a capacity of 250,000 widgets per annum. All other data are assumed to be the same. Calculate the EOQ with gradual replenishment. [5 Marks]
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