Samacheer Kalvi 12th Business Maths Solutions Chapter 10 Operations Research Ex 10.3

Students can download 12th Business Maths Chapter 10 Operations Research Ex 10.3 Questions and Answers, Samacheer Kalvi 12th Business Maths Book Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 12th Business Maths Solutions Chapter 10 Operations Research Ex 10.3

Question 1.
Given the following pay-off matrix (in rupees) for three strategies and two states of nature.
Samacheer Kalvi 12th Business Maths Solutions Chapter 10 Operations Research Ex 10.3 Q1
Select a strategy using each of the following rule (i) Maximin (ii) Minimax
Solution:
(i) Maximin principle
Samacheer Kalvi 12th Business Maths Solutions Chapter 10 Operations Research Ex 10.3 Q1.1
Max (40, -20, -40) = 40. Since the maximum pay-off is Rs.40, the best strategy is S1 according to maximin rule.
(ii) Minimax principle
Samacheer Kalvi 12th Business Maths Solutions Chapter 10 Operations Research Ex 10.3 Q1.2
Min (60, 10, 150) = 10. Since the minimum pay- off is Rs. 10, the best strategy is S2 according to minimax rule.

Samacheer Kalvi 12th Business Maths Solutions Chapter 10 Operations Research Ex 10.3

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.
Samacheer Kalvi 12th Business Maths Solutions Chapter 10 Operations Research Ex 10.3 Q2
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
Samacheer Kalvi 12th Business Maths Solutions Chapter 10 Operations Research Ex 10.3 Q2.1
Max (2000, 3500, 4000) = 4000. Since the maximum profit is Rs. 4000, he must choose crop C as the best crop.
(ii) Minimax principle
Samacheer Kalvi 12th Business Maths Solutions Chapter 10 Operations Research Ex 10.3 Q2.2
Min (8000, 5000, 5000) = 5000. Since the minimum cost is Rs.5000, he can choose crop B and crop C as the best crop.

Samacheer Kalvi 12th Business Maths Solutions Chapter 10 Operations Research Ex 10.3

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.
Samacheer Kalvi 12th Business Maths Solutions Chapter 10 Operations Research Ex 10.3 Q3
What will be the marketing manager’s decision if (i) Maximin and (ii) Minimax principle applied?
Solution:
(i) Maximin principle
Samacheer Kalvi 12th Business Maths Solutions Chapter 10 Operations Research Ex 10.3 Q3.1
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
Samacheer Kalvi 12th Business Maths Solutions Chapter 10 Operations Research Ex 10.3 Q3.2
Min (30, 40, 55) = 30. Since the minimum pay-off is 30 units, the marketing manager has to choose Egg shampoo by minimax rule.

Samacheer Kalvi 12th Business Maths Solutions Chapter 10 Operations Research Ex 10.3

Question 4.
Following pay-off matrix, which is the optimal decision under each of the following rule (i) Maximin (ii) Minimax
Samacheer Kalvi 12th Business Maths Solutions Chapter 10 Operations Research Ex 10.3 Q4
Solution:
(i) Maximin principle
Samacheer Kalvi 12th Business Maths Solutions Chapter 10 Operations Research Ex 10.3 Q4.1
Max (5, 7, 9, 8) = 9. Since the maximum pay-off is 9, the optimal decision is A3 according to maximin rule.
(ii) Minimax principle
Samacheer Kalvi 12th Business Maths Solutions Chapter 10 Operations Research Ex 10.3 Q4.2
Min (14, 11, 11, 13) = 11. Since the minimum pay-off is 11, the optimal decision A2 and A3 according to minimax rule.

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