a company makes three types of candy and packages them in three assortments. Assortment 1 contains 4 cherry, 4 lemon, and 12 lime candies and sells for 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 5,000 cherry, 4,200 lemon and 5,800 lime candies weekly. How many boxes of each type should the company produce each week in order to maximize profit? What is the maximum profit?

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