A landowner of is trying to decide whether to build a playground, a swimming pool, or setup a barbeque corner on the yard. Due to some constraints, she can only afford to build one of these and she needs help in deciding which one to choose. The profitability of each will, to some extent, depend on the weather. If the weather is hot, children would prefer the swimming pool, but if the weather is cool, barbeque will be more profitable. The owner has estimated the annual profitability (in RM'000s) of each option for three states of nature (the weather) as presented in the following Table 4: Swimming pool Playground Barbeque corner Table 4. State of weather Hot 120 70 30 Average 60 90 80 Cool 30 40 115 If the probability of a hot weather is 0.20 and that of a cool weather is 0.45, investigate the best decisions using the following criterions: Expected Value (EV). (i) (ii) Expected Loss Opportunity Value (EOL). (iii) Expected Value of Perfect Information (EVPI). (7 marks) (7 marks) (3 marks)