# Operations Research and Reliability (ISS 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

Essay Question▾

### Describe in Detail

(d) Show that for M/M/1/∞ queue model

where λn and µn 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 j-1or j + 1with the following probabilities:

If there are no… (109 more words) …

## Question number: 2

» Operations Research and Reliability » Finding Solutions in 22, 2xm and Mxn Games

Appeared in Year: 2015

Essay Question▾

### 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… (57 more words) …

## Question number: 3

» Operations Research and Reliability » LPP Computational Methods

Appeared in Year: 2015

Essay Question▾

### Describe in Detail

Solve the following problem Simplex method.

Maximize Z = 8x1+6x2

Subject to

x1+x2 ≤ 10

2x1+3x2 ≤ 25

x1+5x2 ≤ 35

x1, x2 ≥ 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 constraint-equations

• Testing whether it is an optimal solution

• Improving the first trial solution by a set of rules and repeating the process till… (539 more words) …

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