A company makes three types of candy and packages them in three assortments. Assortment I contains 4 cherry , 4 lemon , and 12 lime candies, and sells for a profit of $4.00 . Assortment II contains 12 cherry , 4 lemon , and 4 lime candies, and sells for a profit of $3.00 . Assortment III contains 8 cherry , 8 lemon , and 8 lime candies, and sells for a profit of $ 5.00 . They can make 4 comma 800 cherry , 3 comma 800 lemon , and 5 comma 600 lime candies weekly. How many boxes of each type should the company produce each week in order to maximize its profit (assuming that all boxes produced can be sold)? What is the
