Pole Position, a retailer at Destiny Mall, has a variable cost of $$3$ per lap driven. It has identified two segments of customers: Hard$-$Core drivers and Just$-$For$-$Fun drivers. For simplicity, throughout this problem, assume there is exactly $1$ customer in each of the $2$ segments. Market research shows how each segment values the experience, depending on how many laps are raced:

$\backslash$table$[[$# of Laps,$\backslash$table$[[$Hard$-$Core Total Benefit$],[($$$)$