Knoebels Amusement Park in Elysburg, Pennsylvania, charges a lump-sum fee, L
, to enter its Crystal Pool. It also charges p
per trip down a slide on the pool's water slides. Suppose that 400
teenagers visit the park, each of whom has a demand function of q
1
=
6
−
p
, and that 400
seniors also visit, each of whom has a demand function of q
2
=
3
−
p
. Knoebels' objective is to set L
and p
so as to maximize its profit given that it has no (non-sunk) cost and must charge both groups the same prices. What are the optimal L
and p
?