Aligarh Muslim University (AMU) 2005 B.Tech Information Technology OPERATIONS RESEARCH - Question Paper

OPERATIONS RESEARCH sixth 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) elaborate the slack and surplus variable?
(d) describe symmetric primal and dual? (e) describe an assignment issue
(f) How can we solve a maximization assignment problem?
(g) What do you understand by sensitivity analysis?
(h) describe a symmetric game. Why is it called so?
(i) What is the probability of the queue being non-empty?
(j) If the primal issue has no feasible solution, then the dual will also have no feasible solution. discuss
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 actual. describe 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 obtain the minimum cost of transportation in the subsequent problem:




VI define the ‘revised simplex algorithm, in solving Linear programming issue.
VII (a) Compare the relative advantages and disadvantages of the revised simplex method over the ordinary simplex method.
(b) explain the working principle of ‘Dual simplex method’ in solving a linear programming issue. 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 needed to serve a customer has an exponential distribution with a mean of four minutes. Find: (i) avg. number in the system (ii) the probability that there would be two customers in the queue.
(b) Draw spanning tree for the figure provided below:






IX Write short notes on the following:

PERT and CPM
Minimum Cost Flow issue
Simulation

Earning:   Approval pending.