Exercise 10.3 - Chapter 10 Operations Research 12th Maths Guide Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated On May 15, 2024

By SaraNextGen

Ex $10.3$
Question 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 Solution:
(i) Maximin principle

$\operatorname{Max}(40,-20,-40)=40$. Since the maximum pay-off is Rs. 40 , the best strategy is $S_1$ according to maximin rule.
(ii) Minimax principle

$\operatorname{Min}(60,10,150)=10$. Since the minimum pay- off is Rs. 10 , the best strategy is $\mathrm{S}_2$ according to minimax rule.

Question 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 the only crop, decide which should be his best crop using (i) Maximin
(ii) Minimax
Solution:
(i) Maximin principle

$\operatorname{Max}(2000,3500,4000)=4000$. Since the maximum profit is Rs. 4000, he must choose crop C as the best crop.
(ii) Minimax principle

$\operatorname{Min}(8000,5000,5000)=5000$. Since the minimum cost is Rs. 5000 , he can choose crop B and crop $\mathrm{C}$ as the best crop.

Question 3.
The research department of Hindustan Ltd. has recommended paying the 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? Solution:
(i) Maximin principle

$\operatorname{Max}(10,5,3)=10$. Since the maximum pay-off is 10 units, the marketing manager has to choose Egg shampoo by Maximin rule.
(ii) Minimax principle

$\operatorname{Min}(30,40,55)=30$. Since the minimum pay-off is 30 units, the marketing manager has to choose Egg shampoo by minimax rule.

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

Solution:
(i) Maximin principle

$\operatorname{Max}(5,7,9,8)=9$. Since the maximum pay-off is 9 , the optimal decision is $\mathrm{A}_3$ according to maximin rule.
(ii) Minimax principle

$\operatorname{Min}(14,11,11,13)=11$. Since the minimum pay-off is 11 , the optimal decision $\mathrm{A}_2$ and $\mathrm{A}_3$ according to minimax rule.