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प्रश्न
Following pay-off matrix, which is the optimal decision under of the following rule (i) maximin (ii) minimax
| Act | States of nature | |||
| S1 | S2 | S3 | S4 | |
| A1 | 14 | 9 | 10 | 5 |
| A2 | 11 | 10 | 8 | 7 |
| A3 | 9 | 10 | 10 | 11 |
| A4 | 8 | 10 | 11 | 13 |
उत्तर
| Act | States of nature | Minimum | Maximum |
|||
| S1 | S2 | S3 | S4 | |||
| A1 | 14 | 9 | 10 | 5 | 5 | 14 |
| A2 | 11 | 10 | 8 | 7 | 7 | 11 |
| A3 | 9 | 10 | 10 | 11 | 9 | 11 |
| A4 | 8 | 10 | 11 | 13 | 8 | 13 |
(i) Maximin: Max (5, 7, 9, 8) = 5.
Since the maximum pay-off is 5.
The alternative A1 is selected.
(ii) Minimax: min (14, 11, 11, 13) = 11.
Since the minimum pay-off is 11.
The alternative alternatives A2 and A3 are selected.
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संबंधित प्रश्न
Given the following pay-off matrix(in rupees) for three strategies and two states of nature.
| Strategy | States-of-names | |
| E1 | E2 | |
| S1 | 40 | 60 |
| S2 | 10 | – 20 |
| S3 | – 40 | 150 |
Select a strategy using the following rule (i) Maximin (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
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?
Choose the correct alternative:
Decision theory is concerned with
Choose the correct alternative:
A type of decision–making environment is
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
