OPERATIONS RESEARCH
Q1. A firm can produce three types of clothes say, A, B and C. Three kinds of wool are required font say, red, green and blue. One unit length of type A cloth needs 2 yard of red wool and 3 yards of blue; one unit length of type B cloth needs 3 yards of red wool, 2 yards of green and 2 yards of blue; and one unit length of type C needs 5 yards of green and 4 yards of blue wool. The firm has a stock of only 8 yards of red wool, 10 of green, 15 of blue. It is assumed that the income obtained from one unit length of type A is Rs.3, of type B cloth is Rs.5 and of type C cloth is Rs.4. Formulate LPP and find out how many of cloths of each type to be produced in order to maximize the income.
Q2. Find the IDES to the following transportation problem by VAM method. Also find the optimal plan.
|
1 |
2 |
3 |
4 |
5 |
Available |
| A |
4 |
3 |
1 |
2 |
6 |
80 |
| B |
5 |
2 |
3 |
4 |
5 |
60 |
| C |
3 |
5 |
6 |
3 |
2 |
40 |
| D |
2 |
4 |
4 |
5 |
3 |
20 |
| Required |
60 |
60 |
30 |
40 |
10 |
|
Q3. A) In a-small town, there are only two stores that handle sundry goods - ABC and PQR. The total number of customers is equally divided between the reputation in the community, and they render equally good customer service. Assume that a gain of customers by ABC is loss to PQR and vice versa Both stores plan to run annual pre-Diwali sales during the first week of October. Sales are advertised through local newspaper, radio and television media. With the aid of an advertising firm store ABC constructed the game matrix given below (Figures in matrix represent a gain or loss of customers):
|
Strategy of
ABC
|
|
Strategy of POR
|
|
|
Newspaper
|
Radio
|
Television
|
|
Newspaper
|
30
|
40
|
-80
|
|
Radio
|
0
|
15
|
-20
|
|
Television
|
90
|
20
|
50
|
Determine optimum strategies and the worth of such strategies for both ABC and PQR.
Q3. Discuss the consistency of the following equations and hence solve these equations.
2x1 + 3x2 + 4x3 = 11
x1 -5x2 + 7x3 = 15
3x1 + 11x2 + 13x3 = 25
Q4. An owner of a petrol pump with single attendant wishes to perform a simulation of operations to see whether any improvement is possible. He studied the system and found that an average of 6 customers arrive for service with random arrival times and form a queue, and the attendant provides a service exactly 9 minutes. For simulating the arrival times of customers, he has selected 10 random numbers with expected length of internal equal to one as
| 3.62 |
1.78 |
1.84 |
1.31 |
1.27 |
| 0.14 |
1.71 |
0.77 |
0.97 |
1.32 |
Find (i) The total idle time for the attendant
(ii) Total waiting time for the customers, and
(iii) Maximum queue length during this period.
If the service time is reduced to 6 minutes what is quality of service?
Q5. The Ore Mining Company is attempting to decide whether or not a certain piece of land should be purchased. The land cost is Rs. 3, 00,000. If there are commercial ore deposits on the land, the estimated value of the property is Rs 5, 00,000 If no ore deposits exist, however, the property value is estimated at Rs. 2, 00,000 Before purchasing the land, the property can be cored at a cost of Rs 20,000. The coring will indicate if conditions are favorable or unfavorable for one mining If the coring report is favorable, the probability of recoverable ore deposits on the land is 0.8, while if the coring report is unfavorable the probability is only 0.2. Prior to obtaining any coring information: management estimates that the odds are 50-50 that ore is present on the land. Management has also received coring reports on places of land similar to the one in question and found that 60% of the coring reports were favorable.
Construct a decision tee and determine whether the company should purchase the land, decline to purchase it, or take a coring test before making its decision. Specify the optimal course of action and EMV.
Q6. A maintenance service facility has Poisson arrival rates: negative exponential service times, and operates on a first-come first served queue discipline. Breakdown occurs on an average of three per day with a range of zero to eight. The maintenance crew can service average six machines per day with a range of zero to seven. Find the
a) Mean time in the system
b) Mean number in the system in breakdown or repair
c) Mean waiting time in the queue
d) Probability of finding two machines in the system
e) Expected number in the queue
Q7. Write the short notes on following
a) Models in OR
b) Characteristics of Queuing models