I am having a little trouble converting this problem into a linear programming model and how it affects the constraints.
max-z = |2x1 - 3x2|
s.t. 4x1 + x2 <= 4
2x1 - x2 <= 0.5
x1, x2 >= 0
2026-03-26 22:50:13.1774565413
transforming an absolute value objective function into a linear programming model
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For linear programming problems with only two variables you can easily see what the extreme points are by plotting the feasible region onto a plane.
In your case they look to be $$ \left \{ (0,0), (0, 4), (\frac{1}{4}, 0) (\frac{3}{4}, 1) \right \} $$
When you plug those numbers into your objective function you can easily find which points produce the highest result.