What is operational research? Explain the general method of solving or model. What are the limitations of operational research?
A company combines factor 1 and factor 2 to form a product, which weigh 100 kgs. At least 50KG of factor A and no more than 60KG of factor B. Should be used. Factor 1 cost rupees 25 per kilogram and factor 2 cost rupees 10 per kilogram. Use the simplex method to find the amount of factor 1 and factor 2 which should be used to minimize the cost.
Write Hungarian algorithm to solve the assignment problem.
Given the transportation framework, find the optimal transportation cost.
| From ↓ To→ | A | B | C | D | Plant capacity |
| W | 3 | 2 | 7 | 6 | 5000 |
| X | 7 | 5 | 2 | 3 | 6000 |
| Y | 2 | 5 | 4 | 5 | 2500 |
| Requirement | 6000 | 4000 | 2000 | 1500 |
Discuss queuing process with suitable example of queuing model? Give its assumptions.
Write short notes on (Any two)
a. Kendall's notation
b. Types of inventory system.
c. Importance and advantage of duality problem.
Food manufacturers Company 1 and Company 2 are competing for an increased market share. The payoff matrix shown in the following table describes the increase in market share for Company 1 and decrease in market share for Company 2. Determine optimal strategies for both the companies and the value of the game.
| Company One. | Company 2. | |||
| Give coupons. | Decrease price. | Maintain present strategy. | Increase advertising. | |
| Give coupons. | 2 | -2 | 4 | 1 |
| Decrease price. | 6 | 1 | 12 | 3 |
| Maintain present strategy. | -3 | 2 | 0 | 6 |
| Increase advertising. | 2 | -3 | 7 | 1 |
Attempt any TWO questions
[2x10=20]Solve the duality problem.
Minimize cost Z = 300X₁ + 800X₂
Subject to X₁ + X₂ = 200
X₁ ≤ 40
X₂ ≥ 30
and X₁, X₂ ≥ 0
There are four workers for four tasks to be conducted. Workers have different efficiencies and the task have different difficulty levels. Estimate of profit in rupees for each person is given below. How the task should be allocated to each man so to maximize total earnings?
| Workers | Task 1 | Task 2 | Task 3 | Task 4 |
| A | 5 | 40 | 20 | 5 |
| B | 25 | 35 | 30 | 25 |
| C | 15 | 25 | 20 | 10 |
| D | 15 | 5 | 30 | 15 |
a) Find the cost per period of individual replacement policy of an installation of 3000 light bulbs given in the following.
i. Cost of replacing an individual bulb is RS 20.
ii. Cumulative probability of failure is given below.
| Months | 0 | 1 | 2 | 3 | 4 |
| Cumulative probability of failure. | 0 | 0.1 | 0.3 | 0.8 | 1 |
Calculate the number of light bulbs that would fail during each of the four months.
b) Write The algorithm for solving transportation problem and optimizing using MODI method.