GUJARAT TECHNOLOGICAL UNIVERSITY
ATMIYA INSTITUTE OF TECHNOLOGY AND SCIENCE, RAJKOT
M.C.A. SEM. IV Model Question Paper – 2
640003: Operations Research
MARKS: 70
INSTRUCTIONS:
1. Attempt all the questions.
2.Figurestotherightindicate full marks
3. Assume suitable additional data, if required.
Q.1 
(a) 
I) Explain closeloop in Transportation Problem and its properties.
II) Write an Economic interpretation of ui’s and vj’s. 
5+2 

(b) 
I) Write the dual of following LPP.
Min Z = 12×1 + 8×2 Subject to x1 + x2 >= 3 3×1 + x2 >= 7 x1, x2 >= 0 II) Determine an initial basic feasible solution to the following transportation problem by using a NWCM method. (Ans 12200)

3+4 

Q.2 
(a) 
Define Simulations with its merits and demerits. ExplainMonte CarloSimulations. 
7 

(b) 
Find out the total maximum sales of the following Assignment problem
Sales Person Districts A B C D E 1 32 38 40 28 40 2 40 24 28 21 36 3 41 27 33 30 37 4 22 38 41 36 36 5 29 33 40 35 39 
7 

OR 

(b) 
Determine an initial basic feasible solution to the following transportation problem by using a LCM method. (Ans 180)

5 

Q.3 
(a) 
A firm makes two products X and Y, and has a total production capacity of 9 tonnes per day, X and Y requiring the same production capacity. The firm has a permanent contract to supply at least 2 tonnes of X and at least 3 tonne of Y requires 50 machine hours of production time. The daily maximum possible number of machine hours is 360. All the firm’s output can be sold, and the profit made is Rs. 80 per tonne of X and Rs. 120 per tonne of Y. It is required to determine the production schedule for maximum profit and to calculate this profit. (Use graphical method) 
7 

(b) 
Determine an initial basic feasible solution to the following transportation problem by using a VAM method.

7 

OR 

Q3 
(a) 
Formulate the given LP problem by applying simplex method.
MAX Z= 4x+3y Subject to constraints, 2x+y<=1000 x+y<=800 x<=400 y<=700 and x, y >=0 (140) 
7 

(b) 
Determine an initial basic feasible solution to the following transportation problem by using a MODI method. (Ans. 149, P no 340)

7 

Q4 
(a)

Explain the following terms:
1) Free float 2) ES 3) Looping and Dangling 4) Merge and burst events 5) AOA Vs AON 6) Optimistic time 7) Critical Path 
7 

(b) 
A pipeline is due for repairs. It will cost Rs 10000 and lasts for three years. Alternately, new pipeline can be laid at a cost of Rs 30000 and lasts for 10 years. Assuming cost of capital to be 10 percent and ignoring salvage value, which alternative should be chosen? (p no 794) 
7 







Q5 
(a) 
Use the graphical method to minimize the time needed to process the following jobs on the machines shown, i.e. each machine finds the job which should be done first. Also calculated the total elapsed time to complete both jobs.

7 

(b) 
Construct the network diagram with the following relationship. Find the critical path.
1. A and B are the first activities of the project 2. A and B precede C 3. C precedes D 4. B precedes E and F 5. F and C precedes G 6. E precedes H 7. H precedes I and J 8. D and J precedes K 9. K precedes L 10. G, I and L are terminal activities of the project Activity A B C D E F G H I J K L Duration 5 3 2 1 3 2 8 1 2 3 4 7 (weeks) 
7 


OR 


Q5 
(a) 
1) A company operating 50 weeks in a year is concerned about its stocks of copper cable. This costs rs 240 a meter and there is a demand for 8000 meters a week. Each replenishment costs rs 1050 for administration and rs 1650 for delivery, while holding coss are estimated at 25% of value held a year. Assumng no shortages are allowed what is the optimal inventory policy for the company??
How would this analysis differ if the company wanted to maximize profit rather than minimize cost? What is the gross profit if the company sells cable for rs 360 a meter? (p no 614) II) Explain following keywords:

4
3 

(b) 
A construction company is considering a large building project. The mean time estimates, the variance of these time estimates, manpower requirements and precedence requirement for the various activities are given in the following table:
Activity Immediate Mean time estimates Variance (days squared) Predecessors (days) A – 7 3 B A 5 1 C B 8 5 D A 20 5 E A 11 9 F C, D 7 6 G D 2 4 H D, E 6 4 I F,G,H 10 9 (i) Draw a PERT network for the building project. (ii) Assuming manpower resources are unlimited, find a critical path, as well as the minimum expected completion time. 
7 
===== All The Best =====