A sandwich shop operates on a single$-$period model, making fresh sandwiches every morning before opening. The average underage cost is $$3\mathrm{.}00$ per sandwich, and the average overage cost is $$5\mathrm{.}60$ per sandwich. Based on past data, the number of sandwiches sold on a single day is distributed normally. The average number sold is $52\mathrm{.}1$ sandwiches, with a standard deviation of$7\mathrm{.}8.$ What number of sandriches should the store make in the morning in order to maximize expected profit?