DOEACC Society 2006 DOEACC B Level B10 Applied Operations Research ( ) - Question Paper

BE10-R3: APPLIED OPERATIONS RESEARCH
NOTE:
Time: three Hours Total Marks: 100
1.
a) Formulate the subsequent Diet issue as a linear programming issue. 1 of the
interesting issues in linear programming is that of balanced diet. Dieticians tell us that
a balanced diet must contain certain volumes of nutrients such as calories, minerals
and vitamins etc. Suppose that we are asked to obtain out the food that should be
recommended from a large number of option sources of these nutrients so that the
total cost of food satisfying minimum requirements of balanced diet is the least.
The medical experts and dieticians tell us that are necessary for an adult to consume at
lowest 75 g. of fats and 300 g. of carbohydrates daily. The subsequent table provide the food
items (which are readily available in market), their analysis, and the cost.
Table
Food Food value (gms.) per 100 gm. Cost per kg.
(Rs.)
Proteins Fat Carbohydrates
123456
8.0
18.0
16.0
4.0
5.0
2.5
1.5
15.0
4.0
20.0
8.0
-
35.0
-
7.0
2.5
40.0
25.0
1.00
3.00
4.00
2.00
1.50
3.00
Minimum
Daily
Requirements
75 85 300 -
b) We have 5 jobs, every of which has to go through the machines A and B in the order
AB. Processing times are provided in the table below:
Processing-times in hours
job
12345
Ai
5193
10
BI
26784
Determine a sequence of these jobs that will minimize the total elapsed time T.
c) There is congestion on the platform of a railway station. The trains arrive at the rate of
30 trains per day. The waiting time for any train to hump is exponentially distributed with
an avg. of 36 minutes. compute the following:
BE10-R3 Page one of five January, 2006
1. ans ques. one and any 4 ques. from two to 7.
2. Parts of the identical ques. should be answered together and in the identical
sequence.
i) The mean queue size.
ii) The probability that queue size exceeds nine (obtain the expression).
d) Draw a network diagram for the subsequent set of operations represented by separate
letters.
Operations POST-OPR
A precedes B, C
B precedes D, E
C precedes D
D precedes F
E precedes G
F precedes G
e) A TV repairman obtains that the time spent on his jobs has an exponential distribution with
mean 30 minutes. If he repairs sets in the order in which they come in, and if the arrival
of sets is approximately Poisson with an avg. of 10 per eight hour day, what is the
repairman's expected idle time every day? How many jobs are ahead of the avg. set
just brought in?
f) Show that if dominance occurs in the pay off matrix of a 2´ two game, then there is a
saddle point. Is the converse true?
g) Write the dual of the issue
Max. z = 2x1 + 3x2,+ x3,
4x1 + 3x2 +x3 = 6,

Earning:   Approval pending.