At an Oxford grocery store, the manager Jenny Produce buys lettuce each day to ensure really fresh produce. In her focus on quality, 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 Jenny can buy fresh lettuce for $$7\mathrm{.}00$ a box. The lettuce is sold for $$16\mathrm{.}00$ a box and the dealer that sells old lettuce is willing to pay $$4\mathrm{.}00$ a box. Past history says that tomorrow's demand for lettuce averages $272$ boxes with a standard deviation of $48$ boxes. How many boxes of lettuce should Jenny purchase tomorrow? $($Use Excel's NORMSINV$()$ function to find the Z$-$score. Round intermediate calculations to four decimal places. Round your answer to the nearest whole number.$)$