Question

Question 2

A farmer in the Blue Mountains area of Jamaica wants to decide on the crop to plant next season. He wants to plant either ganja or coffee for export to the USA but need some help. He knows that if he plants ganja and the weather in the USA is predominantly cold he earns $10,000(US per month. If the weather is warm he earns $16,000. If he plants coffee and the weather is cold he earns 13,000 and if the weather is warm he earns $14000. In 40% of the years, the weather was cold and in 60 % the weather was warm.

For $600, he could buy an expert weather forecast from CWD Consulting.

Decision Alternatives	States of Nature with Profits ($) Does not include forecast cost
	Warm weather(W)	Cold weather (C)
Ganja	$16,000	$10,000
Coffee	$14,000	$13000
Prior Probabilities	P(W) = 0.60	P(C) = .40

Conditional probability for a given state of nature where forecasts are either Good (G) or bad (B): That is: P (G|W) = 0.80; P (B|W) = 0.20;P (G|C) = 0.10; P (B|C) = 0.90

After you have computed the revised probabilities round to two decimal places

1. a) Construct the appropriate decision tree to help the farmer make the appropriate decisions. This tree must be constructed in logical order with labels and net payoffs (5 marks). It also includes the revised probabilities (5 marks) (10 marks)

2. b) Fold back the decision tree (5 marks) to determine the best strategy for the farmer; you must state this strategy (1 mark). What is the final expected profit?( 1 mark)(7 marks)

3. c) What is the expected value of sample information(EVSI)- the most that should be paid to seismic testing firm for the test?( 1 mark)

4. d) Calculate the expected value of perfect information (EVPI)- the most that should be paid CWD for prediction of the uncertain outcomes.(1 mark)

5. e) What is the efficiency of sample information?(1 mark)

Answer 1