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March 10th, 2016, 09:24 PM  #1 
Newbie Joined: Mar 2016 From: Milwaukee Posts: 3 Thanks: 0  Linear Programming of Mixed Nut Assortment
Below is a problem on Linear Programming. I think I have a start to it, but I'm in a rut right now so I was wondering if I could receive a little help. Here's the problem A candy store sells three different assortments of mixed nuts containing varying amounts of almonds, pecans, cashews, and walnuts. To preserve the store's reputation for quality, certain maximum and minimum percentages of the various nuts are required for each type of assortment, as shows in the following table. Nut Assortment: Regular Requirements: Not more than 20% cashews, not less than 40% walnuts, not more than 25% pecans, no restriction on almonds Selling price per pound: $0.89 Nut Assortment: Deluxe Requirements: Not more than 35% cashews, not less than 25% almonds, no restriction on walnuts and pecans Selling price per pound: $1.10 Nut Assortment: Blue Ribbon Requirements: Between 30% and 50% cashews, not less than 30% almonds, no restriction on walnuts and pecans Selling price per pound: $1.80 Below is the cost per pound for each nut as well as the max quantity available per week Almonds: $0.45/pound. 2000 lbs available per week Pecans: $0.55/pound. 4000 lbs available per week Almonds: $0.70/pound. 5000 lbs available per week Almonds: $0.50/pound. 3000 lbs available per week The store would like to determine the exact amounts of almonds, pecans, cashews, and walnuts that should go into each weekly assortment to maximize its weekly profit. Here's what I have so far: X1 = The assortment of cashews in the regular mix in pounds X2 = The assortment of walnuts in the regular mix in pounds X3 = The assortment of pecans in the regular mix in pounds X4 = The assortment of almonds in the regular mix in pounds X5 = The assortment of cashews in the deluxe mix in pounds X6 = The assortment of almonds in the deluxe mix in pounds X7 = The assortment of walnuts in the deluxe mix in pounds X8 = The assortment of pecans in the deluxe mix in pounds X9 = The assortment of cashews in the blue ribbon mix in pounds X10 = The assortment of almonds in the blue ribbon mix in pounds X11 = The assortment of walnuts in the blue ribbon mix in pounds X12 = The assortment of pecans in the blue ribbon mix in pounds Cost Constraints (obtained from multiplying cost per pound by max quantity) 0.45(X4+X6+X10) ≤ $900 per week 0.55(X3+X8+X12) ≤ $2200 per week 0.7(X1+X5+X9) ≤ $3500 per week 0.5(X2+X7+X11) ≤ $1500 per week Objective Function This is where I need some help now after thinking about this problem. I can't figure out how to tie in the selling price per pound with the cost per pound for each specific nut. Could anyone provide some clarification? Many thanks. Last edited by maxmatt20; March 10th, 2016 at 09:27 PM. 
March 10th, 2016, 09:28 PM  #2 
Newbie Joined: Mar 2016 From: Milwaukee Posts: 3 Thanks: 0 
The formatting seems to be extremely skewed, but weirdly enough works very rarely. Please let me know if this is an issue for anyone else who is viewing this

March 10th, 2016, 09:29 PM  #3 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,765 Thanks: 623 Math Focus: Yet to find out. 
Funny. This was an assignment in my highschool math class... I probably still have the full written report.

March 10th, 2016, 09:35 PM  #4 
Newbie Joined: Mar 2016 From: Milwaukee Posts: 3 Thanks: 0 
@Joppy That would be of tremendous, tremendous help


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