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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