25. The following matrix gives the payoffs of different course of actions against different states of nature-(pic attached qm1.jpg)

\f22. The following table gives the payoffs of acts A, B, C and the states of nature P, Q, R. The probabilities of the events are 0.2, 0.3 and 0.5 respectively. Calculate EMV and select the best act. A B C P 200 -100 -300 250 300 500 R 300 500 600 {Ans: EMV= 320, Act B} 23. A maker of soft drinks is considering the introduction of a new brand. He expects to sell 50000 to 100000 bottles in a given period according to the following probability distribution: No. Of bottles 50 60 70 80 90 100 sold (in '000) Probability 0.13 0.20 0.35 0.22 0.08 0.02 If the product is launched, he will have to incur a fixed cost of Rs 48000. However, each bottle sold would give him a profit of Rs 1.25. Should he introduce the new brand? {Ans: Yes} 24. The following matrix gives the payoffs of different course of actions against different states of nature. Action Action Action Action Action Action 2 3 4 5 6 N 1 30000 62000 59000 64000 92000 -17000 N 2 63000 80000 100000 38000 92000 11000 N3 -45000 -45000 32000 25000 11000 72000 N 4 93000 10000 -39000 14000 43000 95000 N 5 35000 38000 23000 85000 54000 -9000 Indicate the course of action to be followed under i. Maximax Criteria ii. Maximin Criteria iii. Laplace criteria iv. Hurwitz criteria with coefficient of optimism 0.6 V. Minimax regret criteriaTANS. KS TOU] 21. Following table gives payoffs for actions A1, A2 and A3 corresponding to states of nature $1 and 52 whose chances are 0.6 and 0.4 respectively. A1 A2 A3 51 16 20 18 52 19 15 12 Find decisions under I) Maximin criterion II) EMV criterion (Ans: [)A1 II)