[Math] Linear Programming Word Problem With 3 Variables

linear programmingword problem

A company makes three types of candy and packages them in three assortments. Assortment I contains 4 sour​, 4 lemon​, and 12 lime ​candies, and sells for ​$9.40. Assortment II contains 12 sour​, 4 lemon​, and 4 lime ​candies, and sells for ​$7.60. Assortment III contains 8 sour​, 8 lemon​, and 8 lime ​candies, and sells for $11.00. Manufacturing costs per piece of candy are ​$0.20 for soursour​, ​$0.25 for lemon, and $ 0.30 for lime. They can make 5,200 sour​, 3,800 lemon​, and 6,000 lime candies weekly. How many boxes of each type should the company produce each week in order to maximize its​ profit? What is the maximum​ profit?
I'm struggling with getting these into an equation(s) that I can solve

Best Answer

ass1 [  4s + 4le + 12li =  9.4]
ass2 [ 12s + 4le +  4li =  7.6]
ass3 [  8s + 8le +  8li = 11.0]

s=  0.2
l=  0.25
li= 0.3

I'd guess you would want to put these into a matrix form and then reduce it, 

 4  4  12 | 9.4
12  4   4 | 7.6
 8  8   8 | 11.0
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