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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

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ASSORTMENT 1

Cherry 4

Lemon 4

Lime 12

 

Assortment 2

Cherry 12

Lemon 4

Lime 4

 

Assortment 3

Cherry 8

Lemon 8

Lime 8

 

Maximum for cherry is 4800

Maximum for Lemon 3800

Maximum for Lime 5600

 

Maximum Profit:

P = 4x + 3y + 5z

4x + 12y + 8z <= 4800

4x + 4y + 8z <= 3800

12x + 4y + 8z <= 5600

x, y, z >= 0

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