Railways is bidding on a project that it figures will cost $$300,000$ to perform. To obtain $25\%$ profit, Railways will bid $$375,000,$ netting a profit of $$75,000.$ However, it has been learned that another company, Transrail, is also considering bidding on the project. If Transrail does submit a bid, it will be a bid of $$360,000.$ Railways really wants to win the bid on this project and is considering a bid with only a $15\%$ markup to $$345,000$ to ensure winning regardless of whether or not Transrail submits a bid.

$($a$)$ Given the above scenario, what decision does Railways need to make and what is the state of nature?

$($b$)$ Prepare a profit payoff table from Railways' point of view.

$($c$)$ What decision would be made if Railways used the optimistic approach?

Sorino