How to solve the following system of linear inequalities in x, y and z? x &#x2265;<!-- ≥ -->

quorums15lep

quorums15lep

Answered question

2022-05-11

How to solve the following system of linear inequalities in x, y and z?
x y + z 1.9
y x + z 2.25
z x + y 1.6
x , y , z 0

Answer & Explanation

Skyler Barber

Skyler Barber

Beginner2022-05-12Added 17 answers

one solution is
x = y = z = 0
( x = 0 y = 0 z = 0 ) ( x > 0 ( ( 4 x 5 y < 19 x 18 4 y 5 z 1 10 ( 19 x 10 y ) ) ( y = 19 x 18 z = 1 10 ( 19 x 10 y ) ) ) )
Brooklynn Hubbard

Brooklynn Hubbard

Beginner2022-05-13Added 3 answers

You should use the Simplex Algorithm. I hope you have some kind of mathematical toolbox at your disposal (excel should do it). But you basically should rewrite your problem in the form:
A v = 0
v i 0 ( i )
To assemble the A matrix and v vector:
x y + z 1.9 1.9 x y z 0 1.9 x y z + t 1 = 0 ( t 1 0 )
So the first line of A is [ 1.9 , 1 , 1 , 1 , 0 , 0 ].

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