Elroy Rocket is entering his senior year as an accounting major and has a number of options for his summer break. His options for the $3$ month break follow:

$(1)$ Work full time at a local accounting firm making $$2,200$ per month.

$(2)$ Take a summer class which will cost $$800$ and work half time making $$1,100$ per month.

$(3)$ Take a class at a cost of $$800$ and not work at all during the summer.