Transrail is bidding on a project that it figures will cost $$400,000$ to perform. Using a $25\%$ markup, it will charge $$500,000,$ netting a profit of $$100,000.$ However, it has

been learned that another company, Rail Freight, is also considering bidding on the project. If Rail Freight does submit a bid, it figures to be a bid about $$470,000.$

Transrail really wants this project and is considering a bid with only a $15\%$ markup to $$460,000$ to ensure winning regardless of whether or not Rail Freight submits a bid.

a$.$ Prepare a profit payoff table from Transrail's point of view. $(6$ points$)$

b$.$ For this payoff table find Transrail's optimal decision using $(1)$ the pessimistic approach, $(2)$ the optimistic approach, and $(3)$ minimax regret approach. $(10$ points$)$

c$.$ If Rail Freight is known to submit bids on only $25\%$ of the projects it considers, what decision should Transrail make? $(5$ points$)$

d$.$ Given the information in $($c$),$ what is EVPI? $(5$ points$)$