Question 4 (Tota120 marks) The recent COVID 19 chaos in Hong Kong has triggered Johnson Tam, an entrepreneur, to consider investing in a local surgical mask manufacturing plant. Johnson's problem is to decide how large his plant should be. The annual returns will depend on both the size of his plant and a number of marketing factors related to the health situation of the Hong Kong society . After a careful analysis , Johnson developed the following payoff table : Size of plant Good market ($) Fair market ($) Poor market (Si) Small 100,0 30,0 -10,000 ____ Medium 150,0 50,0 -30,000 ____ Large 200 000 50,0 -70,000 00 Very L arge 300,000 -200,000 00 For example , if Johnson constructs a small plant and the market is good , he will realise a profit of $100,000 . a) Develop a decision table . (4 marks ) b) What is the maximax decision ? (1 mark) c) What is the maximin decision ? (1 mark) d) What is the equally likely decision ? (1 mark) e) Assume each outcome is equally likely, i. Develop a decision tree with the expected monetary value (EMV ) (5 marks ) ii. Calculate the expected value of perfect information (EVPI ) (3 marks ) iii. Help Johnson to write a short note (40 to 50 words )to convince the Board of Di- rectors to buy the perfect information that is available at $30,000 (5 marks )

Question 4.

a)

Decision table is following:

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b)

Using maximax criterion, maximum payoff of each decision is determined and then decision whose maximum payoff is maximum of all, is selected

Maximum payoff of Small plant = MAX(100000, 30000, -10000) = $ 100,000

Maximum payoff of Medium plant = MAX(150000, 50000, -30000) = $ 150,000

Maximum payoff of Large plant = MAX(200000, 50000, -70000) = $ 200,000

Maximum payoff of Very Large plant = MAX(300000, 30000, -200000) = $ 300,000

Maximum of the above Maximum payoffs is $ 300,000 associated with the decision to build Very Large plant

Therefore, maximax decision is to build Very Large plant

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c)

Using maximin criterion, minimum payoff of each decision is determined and then decision whose minimum payoff is maximum of all, is selected

Minimum payoff of Small plant = MIN(100000, 30000, -10000) = $ -10,000

Minimum payoff of Medium plant = MIN(150000, 50000, -30000) = $ -30,000

Minimum payoff of Large plant = MIN(200000, 50000, -70000) = $ -70,000

Minimum payoff of Very Large plant = MIN(300000, 30000, -200000) = $ -200,000

Maximum of the above Minimum payoffs is $ -10,000 associated with the decision to build Small plant

Therefore, maximin decision is to build Small plant

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d)

Using equally likely criterion, average payoff of each decision is determined and then decision whose average payoff is maximum of all, is selected

Average payoff of Small plant = (100000+30000-10000)/3 = $ 40,000

Average payoff of Medium plant = (150000+50000-30000)/3 = $ 56,667

Average payoff of Large plant = (200000+50000-70000)/3 = $ 60,000

Average payoff of Very Large plant = (300000+30000-200000)/3 = $ 43,333

Maximum of the above Average payoffs is $ 60,000 associated with the decision to build Large plant

Therefore, equally likely decision is to build Large plant