Read the following the case and answer the question$($s$)$ that follow $($Total marks $=100)$

MJ Logistics has decided to build a new warehouse to support its supply chain activities. They have the option of building either a large warehouse or a small one. Construction costs for the large facility are R$8$ million versus R$5$ million for the small facility. The profit $($excluding construction cost$)$ depends on the volume of work the company expects to contract for in the future. This is summarized in the table below $($in millions of rand$)$:

PBA$4804$ Decision Support Systems for Managers

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High Volume

Low Volume

Large Warehouse

R$35$

R$20$

Small Warehouse

R$15$

R$9$

The company believes that there is a $60\%$ chance that the volume of demand will be high.

Suppose that the company engages some economic experts to provide their opinion about the future economic conditions. Historically, their upside predictions have been $75\%$ accurate, while their downside predictions have been $90\%$ accurate.

a$)$ Using decision trees, determine the best strategy if the economic experts$$ predictions suggest that the outcome of the market research will be favourable or will be unfavourable. $(60$ marks$)$

b$)$ What is the expected value of sample information $($EVSI$)?(5$ marks$)$

c$)$ What is expected value of perfect information $($EVPI$)?(5$ marks$)$

d$)$ Based on your analysis, provide a corresponding risk profile for the optimal decision strategy $(10$ marks$)$