A city has determined that for a typical unsignalized intersection, a maximum rate of $8$ crashes$/$million entering vehicles can be tolerated. a$)$ At an intersection of $2$ roadways with ADTs of $12,000$ and $7000,$ how many crashes can occur before corrective action must be sought? b$)$ If $10$ rear$-$end crashes, $20$ angle crashes, and $5$ head$-$on crashes were observed at that location during a three$-$year period, determine the relative severity index $($RSI at that intersection using the following crash costs: Rear$-$end: $$15,000,$ Angle: $$45,000,$ Head$-$on: $$60,000.$