Topics
Applications of Matrices and Determinants
Integral Calculus – 1
Integral Calculus – 2
Differential Equations
Numerical Methods
Random Variable and Mathematical Expectation
Probability Distributions
Sampling Techniques and Statistical Inference
Applied Statistics
Operations Research
description
- Meaning
- Situations- Certainty and uncertainty
- Maximin and Minimax Strategy
Related QuestionsVIEW ALL [7]
A person wants to invest in one of three alternative investment plans: Stock, Bonds and Debentures. It is assumed that the person wishes to invest all of the funds in a plan. The pay-off matrix based on three potential economic conditions is given in the following table:
Alternative | Economic conditions | ||
High growth (Rs.) | Normal growth (Rs.) | Slow growth (Rs.) | |
Stocks | 10 | 7000 | 3000 |
Bonds | 8000 | 6000 | 1000 |
Debentures | 6000 | 6000 | 6000 |
Determine the best investment plan using each of following criteria i) Maxmin ii) Minimax
A farmer wants to decide which of the three crops he should plant on his 100-acre farm. The profit from each is dependent on the rainfall during the growing season. The farmer has categorized the amount of rainfall as high medium and low. His estimated profit for each is shown in the table.
Rainfall | Estimated Conditional Profit (Rs.) | ||
Crop A | Crop B | Crop C | |
High | 8000 | 3500 | 5000 |
Medium | 4500 | 4500 | 5000 |
Low | 2000 | 5000 | 4000 |
If the farmer wishes to plant only crop, decide which should be his best crop using (i) Maximin (ii) Minimax
Given the following pay-off matrix(in rupees) for three strategies and two states of nature.
Strategy | States-of-names | |
E_{1} | E_{2} | |
S_{1} | 40 | 60 |
S_{2} | 10 | – 20 |
S_{3} | – 40 | 150 |
Select a strategy using the following rule (i) Maximin (ii) Minimax
The research department of Hindustan Ltd. has recommended to pay marketing department to launch a shampoo of three different types. The marketing types of shampoo to be launched under the following estimated pay-off s for various level of sales.
Types of shampoo | Estimated Sales (in Units) | ||
15000 | 10000 | 5000 | |
Egg shampoo | 30 | 10 | 10 |
Clinic shampoo | 40 | 15 | 5 |
Deluxe shampoo | 55 | 20 | 3 |
What will be the marketing manager’s decision if (i) Maximin and (ii) Minimax principle applied?
Following pay-off matrix, which is the optimal decision under of the following rule (i) maximin (ii) minimax
Act | States of nature | |||
S_{1} | S_{2} | S_{3} | S_{4} | |
A_{1} | 14 | 9 | 10 | 5 |
A_{2} | 11 | 10 | 8 | 7 |
A_{3} | 9 | 10 | 10 | 11 |
A_{4} | 8 | 10 | 11 | 13 |