Operations Research - Dec 2015
Mechanical Engineering (Semester 7)
TOTAL MARKS: 80
TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Assume data if required.
(4) Figures to the right indicate full marks.
Attempt any Four of the followings:
1 (a) Explain the terms - Optimal order quantity, and Lead time.(5 marks)
1 (b) What is Monte Carlo simulation? What types of problems can be solved by it?(5 marks)
1 (c) Explain the following terms with suitable examples - infeasible solution and unbounded solution in the context of Linear programming problem.(5 marks)
1 (d) Write dual of following LPP.
Minimize: Z=20x+10y
Subject to
x+2y ≤40
3x+y ≥ 30
4x+3y=60
x, y≥0.(5 marks)
1 (e) Solve the following games
B | ||||
A | 4 | 1 | 2 | 5 |
7 | 8 | 5 | 9 | |
2 | 0 | 4 | 3 |
Every morning he receives fresh cakes and places order for next day. The order quantity for next day is equal to the number of cakes the demanded on previous day. Assuming that the receives 30 cakes on first day and places order for 30 cakes for next day, simulate the system to determine -
a) Average number of cakes sold per day.
b) Probability of stock out on any day.
c) Average number of unsold cakes per day if he does not sell stale cakes.
d) Average profit per day if he earns profit of Rs.20 per cake and returns unsold cakes next morning with loss of Rs. 10.
Random no 3244 8857 9516 8058 6047 9504 4554 3172 8699 3584
Daily demand | 0 | 10 | 20 | 30 | 40 | 50 |
Probability | 0.02 | 0.08 | 0.15 | 0.40 | 0.30 | 0.05 |
Maximise
X=15 x + 20 y
Subject to
3x+y ≥120
3x+11y ≤ 330
x+y≤ 80
x, y≥0.(10 marks) 3 (b) Five salesman are to be assigned to five territories. Based on the past performance, the following table shows the annual sales (in lakhs) that can be generated by ech salesman in each territory. Find the optimum assignment. ** indicates that Salesman 4 does not wish to work in territory 2.
T1 | T2 | T3 | T4 | T5 | |
S1 | 27 | 15 | 11 | 14 | 10 |
S2 | 32 | 28 | 31 | 15 | 18 |
S3 | 16 | 19 | 16 | 26 | 30 |
S4 | 18 | ** | 22 | 32 | 25 |
S5 | 21 | 20 | 26 | 16 | 12 |
There are 10,000 bulbs in use and it costs Rs.20 to replace an individual bulb which has burnt out at the end of the week. If all bulbs are replaced simultaneously it would cost Rs. 14 per bulb. It is proposed to replace all bulbs at fixed interval of time, irrespective of their status and to continue replacing burnt out bulbs at the end of every week. At what interval should all the bulbs be replaced? What is the average cost of replacement if all the bulbs are replaced as per individual replacement policy? What is the optimal replacement policy?
Week | 1 | 2 | 3 | 4 | 5 |
% failed by the end of week | 5 | 10 | 25 | 35 | 25 |
Distribution Centre | ||||
Plants | w | X | Y | Z |
A | 17 | 20 | 14 | 12 |
B | 15 | 21 | 25 | 14 |
C | 15 | 14 | 15 | 16 |
i)
B | |||
A | 9 | -3 | 2 |
-6 | 7 | -1 | |
-3 | 3 | -4 |
ii)
B | |||||
A | 1 | 3 | 2 | 7 | 4 |
3 | 4 | 1 | 5 | 6 | |
6 | 5 | 7 | 6 | 5 | |
2 | 0 | 6 | 3 | 1 |