# Linear Programming Mixed Assortment of Nuts

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 Cashews:$0.70/pound. 5000 lbs available per week

Walnuts: $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