Question

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’sproblem 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 payofftable:

Size of plant	Good market ($)	Fair market ($)	Poor market ($)
Small	100,000	30,000	-10,000
Medium	150,000	50,000	-30,000
Large	200,000	50,000	-70,000
Very Large	300,000	30,000	-200,000

For example, if Johnson constructs a small plant and the market is good, he will realise a profit of $100,000.

1. Develop a decision table.   (4 marks)

2. What is the maximaxdecision? (1 mark)

3. What is the maximindecision?   (1 mark)

4. What is the equally likely decision?   (1 mark)

5. Assume each outcome isequally likely,

1. Develop a decision tree with the expected monetary value(EMV)    (5 marks)

2. Calculate the expected value of perfect information(EVPI)      (3 marks)

3. Help Johnson to write a short note (40 to 50 words) to convince the Board of Directors to buy the perfect information that is available at $30,000    (5 marks)

Answer 1

a)

Decision table is following:

Size of plant	Good market ($)	Fair market ($)	Poor market ($)
Small	100,000	30,000	-10,000
Medium	150,000	50,000	-30,000
Large	200,000	50,000	-70,000
Very Large	300,000	30,000	-200,000

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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

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