Convert the following problem to a linear program in standard form:

minimze |x|+|y|+|z|,

subject to x+y <= 1

2x+z = 3

So far, I have

x1 = |x|, x = u1-v1, x1 = |u1-v1|

y1 = |y|, y = u2-v2, y1 = |u2-v2|

z1 = |z|, z = u3-v3, z1 = |u3-v3|

Then, minimize x1+y1+z1

Where do I go from here?