Operations Research and Reliability (ISS (Statistical Services) Statistics Paper IV): Questions 1  3 of 3
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Question number: 1
» Operations Research and Reliability » Queuing Models » M/M/1 Model
Appeared in Year: 2015
Describe in Detail
(d) Show that for M/M/1/∞ queue model
where λ_{n} and µ_{n} are the means of Poisson and exponential distributions respectively where there are n people in the system.
Explanation
Suppose the system is in state j at time t. There are j people in the system. In the next time interval of a very small duration Δt, the system can move to state j1or j + 1with the following probabilities:
If there are no
Question number: 2
» Operations Research and Reliability » Finding Solutions in 22, 2xm and Mxn Games
Appeared in Year: 2015
Describe in Detail
Prove that the number of basic variables is a balanced transportation problem is at most , where m is the number of origins and n is the number of destinations.
Explanation
First note that there are in all m + n constraints. We shall show that one of these is redundant so that there are in effect equation in mn variables and hence at most basic variable are there. We note
Summing the m constraints of eq
Question number: 3
» Operations Research and Reliability » LPP Computational Methods
Appeared in Year: 2015
Describe in Detail
Solve the following problem Simplex method.
Maximize Z = 8x_{1}+6x_{2}
Subject to
x_{1}+x_{2 } ≤ 10
2x_{1}+3x_{2} ≤ 25
x_{1}+5x_{2} ≤ 35
x_{1}, x_{2} ≥ 0
Explanation
The Simplex algorithm is an iterative procedure for solving LP problems in a finite number of steps. It consists of

Having a trial basic feasible solution to constraintequations

Testing whether it is an optimal solution

Improving the first trial solution by a set of rules and repeating the process till