# Computer Based Optimization Techniques 2018- MCA 2nd year AKTU

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Paper Id: 214304Roll No. _____________________

MCA

(SEM-III) THEORY EXAMINATION 2018-19

COMPUTER BASED OPTIMIZATION TECHNIQUES

Time: 3 HoursTotal Marks: 70

Note: 1. Attempt all Sections. If require any missing data; then choose suitably.

SECTION A

1. Attempt all questions in brief.2 x 7 = 14

1. What do you mean by Linear Programming? Describe the limitations of L.P.
2. Explain the queuing system transient sate.
3. What is the degeneracy in L.P. Problem.
4. Discuss the Bellman’s principle of optimality.
5. Discuss steady state in terms of Queuing theory.
6. Discuss EOQ with its formula.
7. Differentiate between Slack Variables and Surplus Variables.

SECTION B

2. Attempt any three of the folloing:7 x 3 = 21

1. Use Big-M method to maximize $z = 4x_{1}-x_{2}$ Subject to the constraints:$2x_{1} + x_{2} \geq 6$$x_{1} + 3x_{2} \leq 2$$x_{2} \leq 3$and $x_{1}, x_{2} \geq 0$
2. Develop algorihtm for Vogel’s approximation method for solving transportation problem.
3. What is the dynamic recursive relation? State the ‘principle of optimality’ in dynamic programming and give a mathematical formulation of D.P.
4. Describe the problem of inventory control, when the stochastic demand is uniform, production of commodity is instantaneous and lead time is negligible.
5. What is queuing system? Explain the main characteristics and steady state of queuing system.

SECTION C

3. Attempt any one part of the folloing:
7 x 1 = 7

1. Describe the use and limitaions of Operation Research. Also explain the methodology of operation research.
2. Explain various models and modeling in operation research. When method is best for Operation Research and decision making application?

4. Attempt any one part of the folloing:7 x 1 = 7

1. Explain Degeneracy in Transportation problem. How degeneracy is overcome?
2. Determine the optimum basic feasible solution to the following Transportation problem:
To
From A B C Available
I 50 30 220 1
II 90 45 170 3
III 250 200 50 4
Required 5 2 1

5. Attempt any one part of the folloing:7 x 1 = 7

1. Write short note on the following:
1. Shortest route-problem with example.
2. Maximum flow-problem with example.
2. What is the dynamic programming? State the ‘principle of optimality’ in dynamic programming and give a mathematical formulation of D.P.

6. Attempt any one part of the folloing:7 x 1 = 7

1. A truck has been purchased at a cost of Rs. 1,60,000. The value of truck is depreciated in the first three years by Rs. 20,000 each year and Rs. 16,000 per year thereafter. Its maintenance and operating costs for the first three years are assuming an interest rate of 10%. Find the economic life of the truck.
2. Derive an inventory model with one price break and obtain the decision rules for finding optimal order quantity.

7. Attempt any one part of the folloing:7 x 1 = 7

1. Define the concept of busy period in queuing theory and obtain its distribution for the system $M/M/1.(\infty / FCFS)$. Show that the average length of busy period is $\frac{1}{\mu - \lambda }$
2. Prove that arrival distribution theorem if the arrivals are completely random then the probability distribution of number of arribals are completely random then the probability distribution of number of arrivals in affixed time interval follows a Poisson distribution.

#### Lokesh Kumar

Being EASTER SCIENCE's founder, Lokesh Kumar wants to share his knowledge and ideas. His motive is "We assist you to choose the best", He believes in different thinking.

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