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Posted By: kishore Member Level: Gold Posted Date: 24 May 2008
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2007 Jawaharlal Nehru Technological University M.B.A QUANTITATIVE ANALYSIS FOR BUSINESS DECISIONS Question paper
1. What are the applications of Operations Research in Management?
2. A firm is engaged in breeding pigs. The pigs are fed on various products
grown on the farm. In view of the need to ensure certain nutrient
constituents (call them X, Y and Z). It is necessary to buy two additional
products say A and B. One unit of product A contains 36 units of X and
3 units of Y and 20 units of Z. One unit of product B contains 6 units of
X. 12 units of Y and 10 units of Z. The minimum requirement of X, Y, Z
is 108 units, 36 units and 100 units respectively. Product A costs Rs.20
per unit and B Rs.40 per unit. Formulate the problem and solve it by
corner point method.
3.a) A decision problem has been expressed in the following pay off table
(figures in thousands)
Strategy
State of nature I II III
A 1880 1840 1800
B 1620 1600 1640
C -1400 1420 1720
Suggest course of action under maximax and Maximin Criteria.
b) An electrical goods dealer buys for resale purposes in a market, electrical
item in the range of 0 to 4. He buys 0 or 1 or 2 or 3 or 4 units. These
are his alternative courses of action or strategies. The demand for
electric item in any month is something beyond his control and hence is
a state of nature. Let us presume that the dealer does not know how
many units will be bought from him by the customer. The demand could
be anything from 0 to 4. The dealer can buy each unit at Rs.40 and can
sell it at Rs.45 each, his margin being Rs.5 per unit. Assume stock on
hand is valueless. Give a pay-off table and opportunity loss table.
Contd….2
OR
Code No: 24/MBA(OR) -2-
4. Consider a problem of assigning four clerks. The time (hours) required to
complete the tasks is given below:
Tasks
A B C D
1 4 7 5 6
2 - 8 7 4
Clerks 3 3 - 5 3
4 6 6 4 2
Clerk 2 cannot be assigned to task A and clerk 3 cannot be assigned to
task B. Find all the optimum assignment schedules and calculate the
total hours.
5.a) What is pure strategy in game theory?
b) Solve by stating the strategy of A, strategy of B and value of the game.
Player B
B1 B2 B3 B4 B5
A1 2 4 3 8 4
A2 5 6 3 7 8
A3 6 7 9 8 7
A4 4 2 8 4 3
6. A duplicating machine maintained for office use is used and operated by
people in the office who need to make copies, mostly secretaries. Since
the work to be copied varies in length (number of pages of the original)
and copies required, the service rate is randomly distributed, but it does
approximate a Poisson distribution having a mean service rate of 10 jobs
per hour. Generally the requirement for use are random over the entire
8 hour working day but arrive at a rate of 5 per hour. Several people
have noted that a waiting line develops occasionally and have questioned
the policy of maintaining only one unit. If time of secretary is valued at
Rs.3.50 per hour, make analysis to find:
(i) equipment utilization
(ii) the percent time an arrival has to wait.
(iii) the average system time and
(iv) the average cost due to waiting and operating the machine.
Contd….3
Code No: 24/MBA(OR) -3-
7. A dealer of washing machine keeps stock of Videocon machines.
Previous experience shows the daily demand pattern for the item with
associated probabilities as given below.
Daily Demand in number 0 10 20 30 40 50
Probability 0.01 0.2 0.15 0.5 0.12 0.02
Use the following sequence of random numbers to simulate the demand
for the next 10 days. 25, 39, 65, 76, 12, 05, 73, 89, 19, 49. Also
calculate the average demand.
8. A computer contains 20,000 resistors. When any resistor fails it is
replaced. The cost of replacing a resistor individually is Rs.1. If all the
resistors are replaced at the same time the cost per resistor is reduced to
Rs.0.40. The percent surviving at the end of month ‘t’ and the
probability of failure during the month t are given below:
0 1 2 3 4 5 6
Percent surviving
at the end of t
100 96 90 65 35 20 0
Probability of failure
during the month t
- 0.04 0.06 0.25 0.3 0.15 0.2
What is the optimum replacement plan?
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