Mega$-$Mart, a discount store chain, is to build a new store in Rock Springs. The parcel of land the company has purchased is large enough to accommodate a store with $160,000$ square feet of floor space. Based on marketing and demographic surveys of the area and historical data from its other stores, Mega$-$Mart estimates its annual profit per square foot $($retail and$/$or inventory$)$ for each of the store$$s departments to be as shown in the table below: Department Profit per square foot Men$$s Clothing $$4\mathrm{.}25$ Women$$s Clothing $$5\mathrm{.}10$ Children$$s Clothing $$4\mathrm{.}50$ Toys $$3\mathrm{.}80$ Housewares $$4\mathrm{.}10$ Electronics $$4\mathrm{.}90$ Auto Supplies $$4\mathrm{.}60$ Each department must have at least $16,000$ square feet of floor space, and no department can have more than $20\%$ of the total retail floor space. Men$$s and children$$s clothing, housewares and auto supplies keep all of their stock on the retail floor; however, women$$s clothing, toys and electronics keep some items in back$-$room inventory. Thus, for each of these three departments $10\%$ of the total floor space must be set aside outside of the retail floor space for stocking inventory. For example, if $10,000$ square feet is dedicated to toys then $9,000$ would be retail and $1,000$ inventory space. The profit made in that department would be $$3\mathrm{.}80*9000.$ Find the amount of floor space that should be devoted to each department in order to maximize Mega$-$Mart$$s profit.