Convert the following problem to a linear program in standard form:
minimize |x| + |y| + |z|
subject to x + y ≤ 1
2x + z = 3.
Minimize |x| + |y| + |z|
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Question & Answer: Convert the following problem to a linear program in standard form: minimize…..
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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.