Operation Research SPPU Endsem Question Paper Nov 2022
All 8 questions from this SPPU endsem paper, as printed. Read them here or open the PDF.
- Pattern
- 2019 pattern
- Exam
- Endsem
- Session
- Nov 2022
- Max. marks
- 70
- Time
- 2½ Hours
- Semester
- VII
- Paper code
- [5927]-424
Printed for: B.E. (Mechanical)
Instructions to the candidates
- Answer Q.1 or Q.2, Q.3 or Q.4, Q.5 or Q.6, Q.7 or Q.8.
- Answers in one answer books.
- Figures to the right indicate full marks.
- Assume suitable data, if necessary.
Questions
Q1
- a)[10]
This part has equations that don’t show as text. Open the PDF to read it.
- b)[7]
Write the generalised syntax of LPP and discuss the following terms related to LPP i) Objective function. ii) Constraint surface. iii) Feasible and infeasible points. iv) Optimum solution.
OR- a)
Q2
- a)[10]
This part has equations that don’t show as text. Open the PDF to read it.
- b)[3]
i) Limitations of graphical method. ii) Explain with the help of example conversion of Primal to Dual LPP problem. [4]
Also asked:Nov 2024
- a)
Q3
- a)[8]
Discuss with the help of flow chart Hungarian method to solve the assignment problems.
- b)[10]
This part has equations that don’t show as text. Open the PDF to read it.
OR- a)
Q4
Q5
- a)[12]
A small project involves 7 activities and their times estimates are listed in the following table. Activities are identified by their beginning (i) and ending (j) node numbers. Activities Estimated Duration (Weeks) (i-j) Optimistic Most likely Pessimistic 1-2 1 1 7 1-3 1 4 7 1-4 2 2 8 2-5 1 1 1 3-5 2 5 14 4-6 2 5 8 5-6 3 6 15 i) Draw the network diagram of the activities in the projects. ii) Find expected duration and variance for each activity. What is the expected project length? iii) Calculate the variance and standard deviation of the project length. What is the probability that the project will be completed : 1) At least 4 weeks earlier than expected time. 2) No more than 4 weeks later than expected time. Given Z (0-Z) 1.33 Probability 0.4082
Also asked:Nov 2024
- b)[6]
Explain with example what is looping and Dangling errors in the network.
Also asked:Nov 2024
OR- a)
Q6
- a)[12]
This part has equations that don’t show as text. Open the PDF to read it.
- b)[6]
Explain different types of floats involved in the in CPM analysis of network and how it is calculated during the analysis.
- a)
Q7
- a)[12]
A dentist scheduled all his patients for 30 minute appointments. Some of the patients take more or less than 30 minutes depending on the type of dental work to be done. The following summary shows the various categories of work, their probability and time actually needed to complete the work : Category of service Time required in Minute Probability Filling 45 0.40 Crown 60 0.15 Cleaning 15 0.15 Extraction 45 0.10 Check tip 15 0.20 Simulate the dentist’s clinic for four hours and determine the average waiting time for the patients as well as the idleness of the doctor. Assume that all the patients show up at the clinic at exactly their scheduled arrival time starting at 8 : 00 a.m. Use the following sequence of random numbers to stimulate the above problem. Random Numbers : 40, 82, 11, 34, 25, 66, 17, 79.
- b)[5]
OR- a)
Q8
- a)[12]
A salesman located in a city A decided to travel to city B. He knew the distances of alternative routes from city A to city B. He then drew a highway network map as shown in following figure. The city of origin A. is city 1. The destination city B is city 10. Other cities through which the salesman will have to pass through are numbered 2 to 9. The arrow representing routes between cities and distances in kilometres are located on each route. The salesman problem is to find the shortest route that covers all the selected cities from A to B. The time for each activity is given in the table. (Solve by using Dynamic programming) Activity Duration Activity Duration 1-2 4 4-5 6 1-3 6 4-6 10 1-4 3 4-7 5 2-5 7 5-8 4 2-6 10 5-9 8 2-7 5 6-8 3 3-5 3 6-9 7 3-6 8 7-8 8 3-7 4 7-9 4 8-10 7 9-10 9
- b)[5]
Explain in brief various steps involved in the simulation.
- a)