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What is Operational Research? Explain the general methods for solving OR models.
What do mean by mathematical formulation of LPP? A firm manufactures three products A, B, C. Time to manufacture product A is twice that for B and thrice that for C and to be produced in the ratio of 3 : 2 : 5. The relevant data is given in the following table. If the whole raw material is engaged in manufacturing product A, 1000 units of this product can be produced. There is demand for at least 300, 250, 200 units of products A, B and C and the profit earned per unit is Rs. 50, Rs. 40, Rs. 70, respectively. Formulate the problem as a linear programming problem.
| Raw Material | Requirement per unit of product (Kg) | Total Availability (kg) | ||
|---|---|---|---|---|
| A | B | C | ||
| P | 6 | 5 | 9 | 5000 |
| Q | 4 | 7 | 8 | 6000 |
4. Write an algorithm to maximize the solution of LPP using Simplex method.
Find the optimal solution for the following transportation problem using any methods.
| 1 | 2 | 1 | 4 | 30 |
| 3 | 1 | 3 | 2 | 50 |
| 4 | 2 | 1 | 5 | 20 |
| 20 | 40 | 30 | 9 | 100 |
Write Hungarian algorithm to solve the assignment problem.
Classify the queueing models with example.
Write short notes on (Any Two):
a) EOQ
b) Kendall's Notation for Queueing Model
c) Duality theorem
Attempt any TWO questions
[2x10=20]Using duality to solve the LLP.
Minimize z = 4x₁ + 2x₂ + 3x₃
Subject to 2x₁ + 4x₃ >= 5
2x₁ + 3x₂ + x₃ >= 4 and x₁, x₂, x₃ >= 0
. Define various costs related to inventory. Explain the ABC analysis with better example
a) A Scooter with first cost Rs. 80,000 has depreciation and service pattern as given below:
| Year | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Depreciation during year | 28000 | 20000 | 14000 | 5000 | 4000 | 4000 |
| Annual Service charge | 18000 | 21000 | 25000 | 29000 | 34000 | 40000 |
b) Explain the theory of Two-Person Zero-Sum game with example.