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 $$11\mathrm{.}00$ a box. The lettuce is sold for $$24\mathrm{.}00$ a box and the dealer that sells old lettuce is willing to pay $$3\mathrm{.}00$ a box. Past history says that tomorrow's demand for lettuce averages $275$ boxes with a standard deviation of $45$ boxes.