Problem $5.$ A specialty contractor must decide whether to automate its fabrication process.

Depending on the technological success of the automation project, the results will turn out to be

poor, fair, or excellent. The net payoffs $($i$.$e$.,$ benefits$)$ for these outcomes are $-$$$1,000,000,$

$$400,000$ and $$3,000,000,$ respectively. The initially estimated probabilities that each outcome

will occur are $0\mathrm{.}5,0\mathrm{.}3,$ and $0\mathrm{.}2.$ Should the contact automate its fabrication process? Draw the

decision tree and show your calculations.