A boy has been dating two girls, Mary and Nancy. From experience, he knows that: $(1)$ Mary,

sophisticate, likes to go to more exclusive places where a date $(3$ hours$)$ will cost $$12.$ Nancy,

on the other hand, likes more popular entertainment so that a date $(3$ hours$)$ will cost $$8.(2)$

His budget allows $$48$ per month for dates. His class work leaves a most $18$ hours and

$40,000$ calories of his energy per month for social activities. $(3)$ Each date with Mary

consumes $5000$ calories of energy, but being more vivacious, Nancy takes twice that much. If

he expects $6$ units of pleasure from a date with Mary and $5$ units of pleasure from a date

with Nancy, how must he plan his social life in order to maximize pleasure?