BP has three potential sites where it can build a drilling rig. Due to its past experience, the CEO

has instructed his management team to choose no more than one site.

$T{h}_{\text{u}\text{a}\text{r}\text{r}}$uarr osts, the revenues and the estimated outcomes for each site are given in the table below.

For example, it costs $$8M$ to build a drilling rig in site B$.$ There's a $30\%$ chance for E$1$ with

potential revenue of $$30M$;$50\%$ chance for E$2$ with potential revenue of $$5M$; and a $20\%$ chance

for E$3$ with zero revenue.

Calculate the EMV $(10$ points$).$

How much would the company be willing to pay for perfect information on all three sites

$($together$)?$ Note that after finding out the true nature of each site, the company can still

choose no more than one site. $(15$ points$)$

After a close vote, the company decided not to drill in sites A and B$.$ It was also decided

that site $C$ would be chosen only if it were profitable to drill there. In addition, the

company's CEO determined that site C could not be overflowing $($state E$1).$ Assuming

that is true, how much would the company be willing to pay for perfect information on

site $C$ now? $(10$ points$)$