Set No. 1
Set No. 1
Set No. 1
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Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
?????
1. (a) What is linear programming? What are major limitations and assumptions?
(b) A company produces two types of hats. Each hat of the first type requires
twice as much labour time as the second type. If all hats are of the second
type only, the company can produce a total of 500 hats a day. The market
limits daily sales of the first and second type to 150 and 250 hats. Assuming
that the profits per hat are Rs 8 for type A and Rs 5 for type B, formulate the
problem as a linear programming model in order to determine the number of
hats to be produced of each type so as to maximize the profit. [6+10]
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slack is the difference between the total factory capacity and the total requirement).
Figure 2
Find the optimal transportation plan so as to minimize the transportation cost.
[16]
Year 1 2 3 4 5 6 7 8
Maintenance cost (Rs) 100 250 400 600 900 1,250 1,600 2,000
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When should the machine be replaced? [6+10]
4. (a) In a game of matching coins with two players, suppose A wins one unit of
value when there are two tails and loses 1/ 2 unit of value when there is one
head an one tail. Determine the pay off matrix, the best strategies for each
player and the value of the game to A.
(b) Two players A and B showing each other, put on a table a coin, with head or
tail up. A wins Rs 8 when both the coins show head and Re 1 when both are
tails. B wins Rs 3 when the coins do not match. Given the choice of being
matching player (A) or non-matching player (B) which one would you choose
and what would be your strategy? [8+8]
5. A super market has two girls booking up sales at the counters. If the service time
from each customer is exponential with a mean of 4 minutes, and if people arrive
in a Poisson fashion at the rate of 10 an hour, find
(a) What is the probability of having an arrival has to wait for service?
(b) What is the expected percentage of idle time for each girl? [16]
6. A newspaper boy buys papers from Rs.1.40 and sells them for Rs.2.45 each. He
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cannot return unsold newspapers. Daily demand has the following:
No. of Customers 25 26 27 28 29 30 31 32 33 34 35 36
Probability 0.03 0.05 0.05 0.1 0.15 0.15 0.12 0.1 0.1 0.7 0.6 0.02
If each day’s demand is independent of the previous day?s how many papers he
should order each day? [16]
7. A manufacturing firm has a contract to supply lathe chucks as per the following
schedule. The product made during a month will be supplied at the end of the
month. The setup cost is Rs.1,000, while the inventory carrying cost is Rs.1.00 per
piece per month. In which month should the batches be produced and of what size,
so that the total of setup and inventory carrying costs are minimized? [16]
?????
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Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
?????
2. (a) State the transportation problem. Describe clearly the steps involved in solv-
ing it.
(b) A manufacturer wants to shiploads of his product given in figure 2. The matrix
gives the mileage from origin to destination. Shipping costs are Rs 10 per load
mile. What shipping scheduled should be used? [6+10]
www.andhracolleges.com Figure 2
3. The management of a large hotel is considering the periodic replacement of light
bulbs fitted in its rooms. There are 500 rooms in the hotel and each room has 6
bulbs. The management is now following the policy of replacing the bulbs as they
fails at a total cost of Rs 3 per bulb. The management feels that this cost can
be reduced to Re 1 by adopting the periodic replacement method, on the basis of
information given below, evaluate the alternative and make a recommendation to
the management.
[16]
Months of use : 1 2 3 4 5
Percent of bulbs failing by that month : 10 20 50 80 100
Show that E(x,y)=1-2x(y-1/2) and deduce that in solution of the game the first
player follows a pure strategy while the second has infinite number of mixed strate-
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gies. [8+8]
6. Monthly demand for an item is 200 units. Ordering cost is Rs.350, inventory
carrying charge is 24% of the purchase price per year. The purchase prices are P1
= Rs.10 for purchasing Q1 < 500; P1 = Rs.9.25 for purchasing 500 ≤ Q2 ≤ 750
and P3 = Rs.8.75 for purchasing 750 ≤ Q3 .
Determine optimum purchase quantity. If the order cost is reduced to Rs.100 per
order, compute the optimum purchase quantity. [16]
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3x1 +2x2 +x3 ≥ 60
2x1 +x2 +3x3 ≥ 90 and
x1, x2 , x3 ≥ 0. [16]
?????
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Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
?????
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300, 360 and 190, respectively. Increment unit overtime costs are Rs. 5, Rs. 4 and
Rs. 6, respectively. The current warehouse requirements are 165, 175, 205 and 165,
respectively. Unit shipping costs in rupees between the factories and the warehouse
are given in figure 2.
Determine the optimum distribution for the company to minimize costs. [16]
Figure 2
3. (a) Write a critical essay on replacement problems.
(b) The data collected in running a machine, the cost of which is Rs. 60,000, are
Year : 1 2 3 4 5
Resale value (Rs) : 42,000 30,000 20,400 14,400 9,650
Cost of spares (Rs) : 4,000 4,270 4,880 5,700 6,800
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Cost of labour (Rs) : 14,000 16,000 18,000 21,000 25,000
4. (a) Solve the game whose pay off matrix is given in figure 4a
Figure 4a
(b) Solve the game whose pay off matrix is given in figure 4b.
[8+8]
www.andhracolleges.com Figure 4b
5. A T.V. repairman finds that the time spent on his jobs have an exponential distri-
bution with mean of 30 minutes. If he repairs sets in the order in which they come
in, and if the arrival of sets is approximately Poisson distribution with an average
rate of 10 per 8 hour day, what is repairmen’s expected idle time each day? How
many jobs are ahead of the average set just brought in? [16]
6. A newspaper boy buys papers from Rs.1.40 and sells them for Rs.2.45 each. He
cannot return unsold newspapers. Daily demand has the following:
No. of Customers 25 26 27 28 29 30 31 32 33 34 35 36
Probability 0.03 0.05 0.05 0.1 0.15 0.15 0.12 0.1 0.1 0.7 0.6 0.02
If each day’s demand is independent of the previous day?s how many papers he
should order each day? [16]
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8. What is significance of simulation? Discuss about application of simulation. [16]
?????
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Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All Questions carry equal marks
?????
2. ABC Limited has three production shops supply a product to five warehouse. The
cost of production varies from shop to shop and cost of transportation from one
shop to a warehouse also varies. Each shop has a specific production capacity and
each warehouse has certain amount of requirement. The costs of transportation are
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given below:
I II III IV V Supply
A 6 4 4 7 5 100
B 5 3 7 4 8 125
C 3 4 6 3 4 175
Demand 60 80 85 105 70 400
The cost of manufacturing the product at different production shops is
Find the optimum quantity to be supplied from each shop to different warehouses
at minimum total cost. [16]
3. (a) Discuss in brief about replacement policy for the items that deteriorate with
time.
(b) A plant manager is considering replacement policy for a new machine. He
Year : 1 2 3 4 5 6
Replacement cost at the beginning of year 100 110 125 140 160 190
Resale value at the end of year: 60 50 40 25 10 0
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Operating costs: 25 30 40 50 65 80
4. A company management and the labour union are negotiating a new three-year
settlement. Each of these has 4 strategies.
The costs to the company are given for every pair of strategy choice given in figure
4. [16]
www.andhracolleges.com Figure 4
5. A super market has two girls booking up sales at the counters. If the service time
from each customer is exponential with a mean of 4 minutes, and if people arrive
in a Poisson fashion at the rate of 10 an hour, find
(a) What is the probability of having an arrival has to wait for service?
(b) What is the expected percentage of idle time for each girl? [16]
6. An item is produced at the rate of 50 items per day. The demand occurs at the
rate of 25 items per day. If the setup cost is Rs.100 per setup and holding cost is
Re.0.01 per unit of item per unit of item per day. Find the economic lot size for
one run, assuming that shortages are not permitted. Also find the time of cycle
and minimum total cost for one run. [16]
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8. Define simulation. Discuss about process of simulation. [16]
?????
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