## [SOLVED] Linear Programming - using percentages in constraints

Hi all,

I have a small problem with a linear programming assignment and I was wondering if someone could point me in the right direction.

I have grasped the basics of LP but this question contains %s and I am confused

The question states

"A company produces 2 snacks, Snack A and Snack B, each snack contains chocolate, biscuit and raisins, The company has 100kg of Chocolate, 250kg of biscuit and 300kg of raisins in stock. Snack A must contains at least 40% Chocolate and Snack B must contains at least 20% Biscuit and at least 20% Raisin, each kg of Snack A sells for 40cents and each kg of Snack B sells for 60 cents"

I am not sure how to express the constraints as I have never used "at least %" before

I have come up with the following but I am not sure if it is correct.

X = Snack A
Y = Snack B

Max Z = 40X + 60Y

Subject to

1) .4X + .6Y <= 100 (Chocolate Constaint)
2) .6X + .2Y <= 250 (Biscuit Constraint)
3) .6X + .2Y <= 300 (Raisin Constraint)

X and Y are non-negative

My thinking behind this is that Snack A must have at least 40% Chocolate so the Biscuit and Raisin content can up to 60%, similarly Snack B must contains at least 20% Biscuit and at least 20% Raisin so Chocolate content can up to 60%

As I have said I have no idea whether I am on the right track or not.

Any help would be greatly appreciated.

thanks,
Kone