OPERATIONS RESEARCH - OR Paper 1

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OPERATIONS RESEARCH 6th Semester IT 210 (MAY 2005)
I (a) What is the condition that a set of m linear equations with n variable Ax = b be consistent?
(b) What is the necessary and sufficient condition for a solution set of a linearly independent set of equations to be a basic solution?
(c) What are the slack and surplus variable?
(d) Define symmetric primal and dual? (e) Define an assignment problem
(f) How can we solve a maximization assignment problem?
(g) What do you understand by sensitivity analysis?
(h) Define a symmetric game. Why is it called so?
(i) What is the probability of the queue being non-empty?
(j) If the primal problem has no feasible solution, then the dual will also have no feasible solution. Explain
II What do you mean by consistent solutions? Under what condition a set of linear equations will be consistent? Prove that a set of linearly independent set of equations are consistent but the converse is not necessarily true. Define a basic solution of a system of m independent linear equations with n unknowns.
III If a LPP admits an optimal solution, the objective function assumes the optimum value at an extreme point f the convex set generate3d by the et of all FS.
IV Solve the LPP by Simplex Method:
Maximize z=3x1 + 2x2
Subject to 2x1 + x2 ≤ 12
6x1 + 5x2 ≤ 40 and x1, x2 ≥ 0
V Find the minimum cost of transportation in the following problem:

VI Describe the ‘revised simplex algorithm, in solving Linear programming problem.
VII (a) Compare the relative advantages and disadvantages of the revised simplex method over the ordinary simplex method.
(b) Discuss the working principle of ‘Dual simplex method’ in solving a linear programming problem. Why is the method called as dual simplex method?
VIII (a) Customers arrive at a post office manned by a single person according to Poisson input process with mean rate of 10 per hour. The time required to serve a customer has an exponential distribution with a mean of 4 minutes. Find: (i) average number in the system (ii) the probability that there would be 2 customers in the queue.
(b) Draw spanning tree for the figure given below:

IX Write short notes on the following:

• PERT and CPM
• Minimum Cost Flow Problem
• Simulation