large amusement parks

between D and E, would go with E.

the live shows seem to be targetted at diverting excess crowds at lunch and attracting enough for supper or in other words just the right capacity/optimal utilization of the restaurant

the blank space should ideally convey the unified goal.

Lets look at options:

A) keeping the lines at the various rides short by drawing off part of the crowd [whether the live performances ease the lines at rides in not mentioned in the passage. this can be categorized as out of scope]

(B) enhancing revenue by attracting people who come only for the live shows and then leave the park [if live performances attract people and retain them rather than leave the park then in lunctimes restaurants would be even more crowded. the purpose would be defeated. eliminated!]

(C) avoiding as far as possible traffic jams caused by visitors entering or leaving the park [traffic jams is not discussed in the stimulus at all. eliminated!]

(D) encouraging as many people as possible to come to the park in order to eat at the restaurants [ there is a slight hitch in this. we do not know if the live performances encourage people to come to the park to eat at the restaurants. we know that live performances manage the crowd that has turned up well. eliminated!]

(E) utilizing the restaurants at optimal levels for as much of the day as possible [ correct! it clearly mentions how at lunchtime live performances take away the crowd from the restaurants and keep the crowd for supper]

Hope this helps!