Your firm is considering bidding on a project. The estimated cost of the project is $$500,000.$

You are considering bids of $$550,000,$ $$600,000,$ and $$650,000,$ with respective probabilities of winning the bid at $0\mathrm{.}8,0\mathrm{.}6,$ and $0\mathrm{.}3.$

$($a$)$ Which bid maximizes expected profit?

$($b$)$ If costs could be $$450,000$ or $$550,000($equally likely$),$ how does this affect your

bid choice?

$($c$)$ What is the value of knowing the exact cost before bidding?