The menus are determined either by a school or system wide basis.

Many schools particularly those of a higher level have student s participate in making up the menus. The federal government provided free foo to the schools. To an extent the menus are determined by the food that is available. Very frequently the state has guidelines for healthy meals and the schools obey since most lunches are subsidized even for students who do not receive free or reduced price meals.

Another item is that food tends to be cheaper at certain times. That is taken into consideration.

Many foods that schools receive are precooked or frozen, I think that there is very little use of recipes for that reason. It is mainly ordering and menu planning based on local, state and federal regulations.