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

Essay Question▾

Describe in Detail

(d) Show that for M/M/1/∞ queue model

Equation

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:

Equation

Equation

Equation

Equation

Equation

If there are no

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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 Equation , 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 equation in mn variables and hence at most Equation basic variable are there. We note

Equation

Equation

Summing the m constraints of eq

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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

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