$2.$ The local supermarket buys lettuce each day to ensure really fresh produce. Each morning, any lettuce that is left from the previous day is sold to a dealer that resells it to farmers who use it to feed their animals. This week, the supermarket can buy fresh lettuce for $$4\mathrm{.}00$ a box. The lettuce is sold for $$10\mathrm{.}00$ a box and the dealer that sells old lettuce is willing to pay $$1\mathrm{.}50$ a box. There is no disposal fee. Past history says that tomorrow's demand for lettuce averages $300$ boxes with a standard deviation of $47$ boxes.

How many boxes of lettuce should the supermarket purchase just for tomorrow?