# Thread: Complex Problem with Linear Constraints & Gauss-Jordan

1. ## Complex Problem with Linear Constraints & Gauss-Jordan

Suppose you're looking to buy 20 of A, 30 of B, 35 of C

Pack 1 (x1) comes with 4A, 8B, & 8C
Pack 2 (x2) comes with 5A, 4B, & 10C

Assumptions: Fractions of packs are allowed

Question 1: Assuming you're looking to buy exactly 20A, 30B, and 35C, is there any way of doing this using a combination of pack 1 and pack 2 orders? Show results using the Gauss-Jordan method

I did the following (assume the comma means a break between each row): [ 4 5, 8 4, 8 10] * [x1, x2] = [20, 30, 35]

And ended up with [1 5/4, 0 -6, 0 0] * [x1, x2] = [5, -10, -5]

Which is supposed to mean there's no solution. Not sure if i did this right or not.

Question 2: Now assume you have to order at least 20A, 30B, and 35C. Model the problem as a system of 3 equations with 5 variables, pack 1 (x1), pack 2 (x2), remainder of A, remainder of B, remainder of C

No idea how to do this or solve for this with the Gauss Jordan method