Sid's summer job is working at a roadside stand that specializes in homemade ice cream. The manager asks Sid to order small plain cones and extra-large sugar cones. The storage room will hold at most 12 boxes of cones. A box of small plain cones costs $30 and a box of extra-large sugar cones costs $90 dollars. A maximum of $800 is budgeted for this purchase of cones. (a) Using x for the number of boxes of plain cones and y for the number of
boxes of sugar cones, translate the conditions of the problem into a system of inequalities.

(b) Graph this system of inequalities and shade the feasible region for this
problem. Identify the vertices of the region by specifying their coordinates.