1. Problems Decision Making under Uncertainty Rahul Chandra

2. Question A food product company is introducing a new product. Three different alternate course of actions (strategies) are available to the company. These are-  Launch at a High Price (S 1 )  Launch at a Moderate Price (S 2 )  Launch at a low Price (S 3 ) Rahul Chandra

3. Question Three different states of Nature are also identified as,  High Sales (N 1 )  Moderate Sales (N 2 )  Low Sales (N 3 ) Marketing department has also worked out the payoffs in terms of profits for each strategies and States of Nature. Rahul Chandra

4. Question Payoff Matrix Strategies States of S 1 S 2 S 3 Nature N 1 7,00,000 5,00,000 3,00,000 N 2 3,00,000 4,50,000 3,00,000 N 3 1,50,000 0 3,00,000 Select the Optimum Strategy using, Maximax Criterion, Maximin Criterion, and Laplace Criterion Rahul Chandra

5. Maximax Criterion Strategies States of S 1 S 2 S 3 Nature N 1 7,00,000 5,00,000 3,00,000 N 2 4,50,000 4,00,000 3,00,000 N 3 1,50,000 100,000 0 Maximum Of Strategy 7,00,000 5,00,000 3,00,000 Rahul Chandra

6. Maximin Criterion Strategies States of S 1 S 2 S 3 Nature N 1 7,00,000 5,00,000 3,00,000 N 2 3,00,000 4,50,000 3,00,000 N 3 1,50,000 0 3,00,000 Minimum Of Strategy 1,50,000 0 3,00,000 Rahul Chandra

7. Laplace Criterion  It attaches equal weight age to each state of Nature. Therefore expected payoffs ( Calculated as simple average for all strategies ) would be, Strategies States of S 1 S 2 S 3 Nature N 1 7,00,000 5,00,000 3,00,000 N 2 3,00,000 4,50,000 3,00,000 N 3 1,50,000 0 3,00,000 Expected 3,83,333 3,16,666 3,00,000 payoff Rahul Chandra

8. Question  An Investor is given the following investment alternatives and rate of returns as follows: Market Conditions Low Medium High Regular Shares 7% 10% 15% Risky Shares -10% 12% 25% Real State -12% 18% 30% Rahul Chandra

9. Question Use Maximax Criterion, Maximin Criterion, and Laplace Criterion to suggest the best alternative course of action. Rahul Chandra

10. Problems Decision Making under Risk Rahul Chandra

11. Question The Manager of a flower shop purchases flowers on a previous day and delivers it to its customer other day on their order. Flowers are purchased at Rs10/- per dozen and are sold at Rs30/-. All unsold flowers are donated to a Hospital free of cost. On the bases of previous experience the probability distribution of Sales is worked out as, Rahul Chandra

12. Question Total Sales: 70 80 90 100 ( in dozens ) Probability : 0.1 0.2 0.4 0.3 Suggest how many dozens of flowers should be purchased to optimize the profits? Also find out optimum expected profits? Rahul Chandra

13. Solution Profit on sales: Rs30/ - Rs10/ = Rs20/- Loss on Unsold Flower = Rs10/- Rahul Chandra

14. Solution Conditional Profit Matrix State of Course of action Nature 70 80 90 100 70 1400 1300 1200 1100 80 1400 1600 1500 1400 90 1400 1600 1800 1700 100 1400 1600 1800 2000 Rahul Chandra

15. Solution Expected Payoff Table State of Prob. Course of action Nature 70 80 90 100 70 0.1 140 130 120 110 80 0.2 280 320 300 280 90 0.4 560 640 720 680 100 0.3 420 480 540 600 EMV 1400 1570 1680 1670 Rahul Chandra

16. Solution  Finally highest EMV is attached with course of action of 90, that means Manager will purchase 90 flowers each day.  Expected optimum profits would be Rs1680/-. Rahul Chandra

17. Question  A retailer purchases Cherries at Rs50/- and sells them for Rs80/- per piece. Unsold are disposed of the next day at a salvage value of Rs20/-. Passed sales (of 120 days) have shown the following patterns:  Pieces Sold : 15 16 17 18  No. of Days: 12 24 48 36 Find out the Optimum pieces to be purchased each day in order to Optimize the profits. Rahul Chandra

18. Problems Game Theory Rahul Chandra

19. QUESTION 1 b1b2b3b4b5 a13-1467 a2-182412 a316861412 a4111-421

20. QUESTION 1 b1b2b3b4b5 a13-1467-1 a2-182412-1 a316861412 6 a4111-421-4 161161412 6

21. Solution  Saddle point exist  Value of Game = 6  Optimum Strategy: a3, b3 Rahul Chandra

22. QUESTION 2 b1b2b3b4 a11734 a25645 a37203

23. QUESTION 1 b1b2b3b4 a11734 1 a25645 4 a37203 0 7 7 4 5 4

24. Solution  Saddle point exist  Value of Game = 4  Optimum Strategy: a3, b3 Rahul Chandra

25. QUESTION 3 b1b2b3b4 a135 35255 a23020150 a34050010 a455601015

26. QUESTION 3 b1b2b3b4 a135 352555 a230201500 a340500100 a45560101510 55 60 25 15

27. Solution  Saddle point does not exist  Value of Game = ?  Optimum Strategy: ? Rahul Chandra

28. Principle of Dominance b1b2b3b4 a135 35255 a23020150 a34050010 a455601015 a1 dominates a2 Rahul Chandra

29. a1 dominates a2 b1b2b3b4 a135 35255 a23020150 a34050010 a455601015 Rahul Chandra

30. b1 dominates b2 b1 b2 b3b4 a135 35 255 a340 50 010 a455 60 1015 Rahul Chandra

31. b4 dominates b1 b1 b3b4 a135 25 5 a340 010 a455 1015 Rahul Chandra

32. a4 dominates a3 b3b4 a1 25 5 a3 010 a4 1015 Rahul Chandra

33. Final Matrix b3 b4 a1 25 5 a4 10 15 Rahul Chandra

34. QUESTION 4 b1b2b3 a155 4035 a2707055 a3755565

35. QUESTION 5 b1b2b3 a1 8 4-2 a2-2-1 3

36. QUESTION 6 b1 b2 a1-6 7 a2 4 -5 a3-1 -2 a4-2 5 a5 7 -6