JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III OPERATIONS RESEARCH Previous Question Paper (January/February - 2023 - R18)
Note: i) Question paper consists of Part A, Part B. ii) Part A is compulsory, which carries 25 marks. In Part A, Answer all questions. iii) In Part B, Answer any one question from each unit. Each question carries 10 marks and may have a, b as sub questions.
Part A
How you can identify the unbounded solution in simplex method.
Answer
In the simplex method, an unbounded solution is identified during the ratio test when all entries in the pivot column are either negative or zero. This indicates that there are no positive values to calculate the minimum ratio, meaning the entering variable can be increased indefinitely without violating the feasibility constraints, thus causing the objective function value to increase (or decrease) without bound.
Define linear programming.
Answer
Linear programming is a mathematical optimization technique used to determine the best possible outcome in a model whose requirements are represented by linear relationships. It involves maximizing or minimizing a linear objective function subject to a set of linear constraints in the form of equalities or inequalities.
The standard model is expressed as:
Subject to:
This method is widely applied in resource allocation, production planning, and logistics to achieve optimal efficiency under limited resources.
Name the methods to find initial feasible solution for transportation problem.
Answer
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How you can convert maximization assignment model in to minimization problem?
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Write the conditions to find sequence for n jobs 3 machines problem.
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Write the procedure to find average cost for replacement when money value is not changing.
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Write the characteristics of game theory.
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Briefly explain pure strategy, mixed strategy, and optimal strategy.
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Define dynamic programming.
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Write the formulae to find out length of queue and length of system for (M/M/1): (FCFS/∞) model.
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Part B
Solve the following LPP using simplex method Max Z = 6x1+ 4x2 Subjected to 2x1 + 3x2 ≤ 30, 3x1+2x2 ≤ 24, x1+x2 ≥ 3, x1 ≥ 0, x2 ≥ 0.
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Use two phase method to solve the following LPP Min Z = 5x+ 6y Subjected to 2x + 5y ≥ 1500, 3x + y ≥ 1200, x ≥ 0, y ≥ 0.
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Trans bulk company has three warehouses A, B and C of capacities 50, 60 and 40 respectively and four stores P, Q, R and S of capacities 20, 50, 70 and 10 respectively. Cost (in hundreds of rupees) of shipping one unit of commodity from various warehouses to different stores are as follows:
| Warehouse | P | Q | R | S |
|---|---|---|---|---|
| A | 5 | 15 | 7 | 6 |
| B | 8 | 7 | 9 | 1 |
| C | 15 | 9 | 8 | 8 |
Answer
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Four engineers are available to design four projects. Engineer 2 is not competent to design the project B. Given the following estimates needed by each engineer to design a given project, find how should the engineers be assigned to projects so as to minimize the total design of four projects.
| Engineer | A | B | C | D |
|---|---|---|---|---|
| 1 | 12 | 10 | 10 | 8 |
| 2 | 14 | Not suitable | 15 | 11 |
| 3 | 6 | 10 | 16 | 4 |
| 4 | 8 | 10 | 9 | 7 |
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Four jobs are to be processed in order on each of the three machines, you are required to set up an operation plan that minimizes the elapsed time and idle time of the system.
| Jobs | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| P | 12 | 10 | 10 | 11 |
| Q | 9 | 8 | 7 | 7 |
| R | 10 | 9 | 8 | 8 |
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Write a note on replacement of capital items when money value is considered.
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The following table gives the running costs per year and resale price of a certain equipment whose purchase price is Rs 5000. At what year is replacement due?
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Solve the game whose pay of matrix is given below by using graphical method.
| A/B | I | II | III | IV |
|---|---|---|---|---|
| I | 1 | 4 | -2 | -3 |
| II | 2 | 1 | 4 | 5 |
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A manufacturing company purchases 9000 parts of the machine for its annual requirements, ordering one month usage at time. Each part costs 20 Rs/-. The ordering cost per order is 15 Rs/- and carrying charges are 15% of the average inventory per year. Find out a more economical purchasing policy for the company.
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Solve the following LPP by using dynamic programming Maximize Z = 3x1 + 8x2 Subjected to x1 + 4x2 ≤ 8, x2 ≤ 2, x1, x2 ≥ 0.
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In a bank single cash counter is operated for drawing money. On average 40 persons arrive in a 4 hour day. Each cashier is to spend 10 minutes on the average on an arrival. If the arrivals are Poisson distributed and service times are according to exponential distribution. Determine: a) Average number of customers in the system. b) Average number of customers waiting in the system. c) Average time a customer spends in the system. d) The probability that a customer has to wait before he gets service.
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