Question & Answer: Convert the following problem to a linear program in standard form: minimize…..

Minimize |x| + |y| + |z|

Subject to x + y < 1

2x + z = 3

Here, in this problem, x, y, z variables should be free. They can be defined as –

x = x1 – x2 x1, x2 > 0

y = y1 – y2 y1,y2 > 0

z = z1 – z2 z1,z2 > 0

Then linear program becomes,

Minimize x1 + x2 + y1 + y2 + z1 + z2

Subject to x1 – x2 + y1 – y2 + s = 1

2×1 – 2×2 + z1 – z2 = 3

x1,x2,y1,y2,z1,z2,s > 0

Any optimization problem with linear objective and constraints can be transformed into the standard form.