$1.$ Your engineers are developing a new product to launch next year that will require both software and hardware innovations. The software team requests a budget of $$5$ million and forecasts an $79\%$ chance of success. The hardware team requests a $$8$ million budget and forecasts a $52\%$ chance of success. Both teams will need $6$ months to work on the product, and the risk$-$free interest rate is $4\%$ APR with semiannual compounding. a$.$ Which team should work on the project first? b$.$ Suppose that before anyone has worked on the project, the hardware team comes back and revises their proposal, changing the estimated chance of success to $78\%$ based on new information. Will this affect your decision in $($a$)?$

a$.$ Which team should work on the project first?

$$ The $($hardware OR software$)$ team should work first, followed by the $($hardware OR software$)$ team.

b$.$ Suppose that before anyone has worked on the project, the hardware team comes back and revises their proposal, changing the estimated chance of success to $78\%$ based on new information. Will this affect your decision in $($a$)?$

$($Yes OR No$),$ the $($hardware OR software$)$ team should work first, followed by the $($hardware OR software$)$ team.