Exercise 10.3: Decision Theory

Exercise 10.3

1. Given the following pay-off matrix(in rupees) for three strategies and two states of nature.

Select a strategy using each of the following rule (i) Maximin (ii) Minimax

2. 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.

If the farmer wishes to plant only crop, decide which should be his best crop using (i) Maximin (ii)Minimax

3. 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-offs for various level of sales.

What will be the marketing manager’s decision if (i) Maximin and (ii) Minimax principle applied?

4. Following pay-off matrix, which is the optimal decision under each of the following rule (i) maxmin (ii) minimax

Answers:

1. (i) S1 (ii) S2 

2. (a) Crop C (b) Crop B and Crop C

3. (i) Egg shampoo (ii) Egg Shampoo 

4. (i) A1 and A3 (ii) A2 and A3