Knoebels Amusement park charges a lump-sum fee, L, to enter its Crystal Pool. It also charges p per trip down the slide on the pool's water slides. Suppose that 350 teenagers, each of whom has a q1=6-p, and that 350 seniors also visit, each of whom has a demand function of q2=5-p. Knolebel's 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 price. Whatare the optimal L and p?

Please explain how to solve this problem in detail. Thank you!