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 350 seniors also visit, each of whom has a demand function of q_2 = 3 - p. Knoebels'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 prices. Required:
What are the optimal L and p?