The Carter Nut Company supplies a variety of nut mixtures for sale to companies that package and resell them. Its most expensive product is Bridge Mix, a mixture of peanuts, almonds, and cashews. Bridge Mix contains no more than 25% of peanuts and no less than 40% cashews. There is no limitation on the percentage of almonds. The current selling price of Bridge Mix is $0.80 per pound. CNC estimates that it can process up to 1000 pounds of Bridge Mix this month. The table gives the amounts of inventory and cost of the nuts to be used.
Type Cost($per lb) Pounds available
Peanuts 0.20 400
Almonds 0.35 250
Cashews 0.50 200
So currently I am working on just setting up this Linear Programming Problem. Thus far, I have not had a problem setting these problems up, but I am hung up on this example in terms of the constraints.
My decision variables are:
x1 = number of pounds of peanuts
x2 = number of pounds of almonds
x3 = number of pounds of cashews
My objective function is: Maximize Profit
P = 0.20x1 + 0.35x2 + 0.50x3
The Constraints I understand are: (at least I think I'm right so far)
x1 + x2 + x3 ≤ 1000
And x1,x2,x3 ≥ 0 (non-negativity)
I know I am missing some constraints from the information in this question, but I am confused on how to put them together. It seems in this example there needs to be some work done to just figure out the constraints. The previous examples I have done have not required this. If I could get a couple hints here I would greatly appreciate it. Thanks.