The systems engineering project manager for ICE company is currently faced with the question of whether to award a $$100,000$ contract to PENGUIN software company. The project manager has three internal ratings $($poor risk, average risk, and good risk$)$ for evaluation of a contractor, but does not know which category fits the PENGUIN software company. Internal ratings indicate that $40\%$ of similar companies are poor risks, $15\%$ are average risks, and $45\%$ are good risks. If contract is awarded, the expected profit for poor risk is $$1000,$ for average risk $$100,000,$ and for good risk $$2,000,000.$ If contract is not awarded, the ICE company expected payoff is $$0.$

$\backslash$table$[[,$State of Nature$/$Probability$,],[$Alternatives$,$Poor Risk,Average Risk,Good Risk$],[$Award Contract to SW software,$40\%,15\%,45\%$