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What is operational research? Explain the general methods of solving OR model.
A chair manufacturing company produces two types of chairs A and B using three machines, X, Y and Z. The time required for each chair on each machine and the maximum time available on each machine for a given below:
| Machine | Time required for each type | Maximum time available |
|---|---|---|
| A | B | Per week in hrs | |
| X | 6 | 8 | 120 |
| Y | 3 | 5 | 100 |
| Z | 12 | 4 | 144 |
Write an algorithm to minimize the solution of LPP using simplex method.
Given the transportation framework, find the optimal solution
| From | To → A | B | C | Plant Capacity |
|---|---|---|---|---|
| X | 1 | 2 | 1 | 160 |
| Y | 7 | 1 | 160 | 240 |
| Z | 2 | 160 | 35 | 35 |
| Requirement | 65 | 35 | 35 | 115 |
Find the cost per period of machine replacement policy of an installation given in the following table. The $200 street lamps
a. Cost of replacing individually bulb is given in table
b. Cumulative probability of failure is given below
| Week | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| Cumulative probability of failure | 0 | 0.1 | 0.3 | 0.5 | 0.7 | 1.0 |
Discuss single channel queuing model with suitable example? Give its assumptions.
Write short notes on (any two)
a. Kendall's notation
b. Big M method
c. Importance and advantage of duality problem
Attempt any TWO questions
[2x10=20]Solve duality to solve the LLP Minimize z = 20x₁ + 40x₂
Subject to 3x₁ + 6x₂ ≥ 600
5x₁ + 12x₂ ≥ 36
20x₁ + 10x₂ ≥ 100
and x₁, x₂ ≥ 0
A City Corporation has decided to carry out Maintenance work on city. There are four tasks to be completed using 5 contractors. Which of these contractors should be assigned those tasks? Solve the assignment problem to get best result.
| Contractor | Task 1 | Task 2 | Task 3 | Task 4 |
|---|---|---|---|---|
| A | 19 | 24 | 37 | 28 |
| B | 18 | 37 | 28 | 39 |
| C | 19 | 28 | 31 | 26 |
| D | 30 | 16 | 28 | 30 |
| E | 20 | 25 | 31 | 26 |
a) Two types of food manufacturers are competing for an increased market share. The payoff matrix describes the increase in market share of A and decrease of share of B. Determine optimal strategies for both the manufacturers and the value of the game.
| A \ B | Give Price | Decrease Price | Maintain present strategy | Increase Advertising |
|---|---|---|---|---|
| Give Price | 25 | 20 | 14 | 8 |
| Decrease Price | 27 | 16 | 12 | 14 |
| Maintain present strategy | 35 | 8 | 15 | 6 |
| Increase Advertising | -2 | 8 | 13 | 5 |