A factory manufactures doodads and whirligigs. It costs $2 and takes 3 hours to produce a doodad. It costs $4 and takes 2 hours to produce a whirligig. The factory has $220 and 150 hours this week to produce these products. If each doodad sells for $6 and each whirligig sells for $7, then how many of each product should be manufactured this week in order to maximize profit?