Knoebels Amusement Park in Elysburg, Pennsylvania, charges a lump-sum fee, L, to enter its Crystal Pool

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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 450 visit the park, each of whom has a demand function of q1=6− p, and that 450 seniors also visit, each of whom has a demand function of q2=5−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. What are the optimal L and p?

The optimal L and p are

L= $______ and p= $______. (Enter numeric responses using real numbers rounded to three decimal places.)