mixed system of equalities and inequalities, for example: x + 2 y + 3 z...

glitinosim3

glitinosim3

Answered

2022-06-30

mixed system of equalities and inequalities, for example:
x + 2 y + 3 z = 10 2 x + 4 y + 10 z = 20 4 x + y + z < 10
where unknown variables x , y , z are all real-valued.
How can get a solution (or the range of all feasible solutions) for this system?

Answer & Explanation

Jordin Church

Jordin Church

Expert

2022-07-01Added 11 answers

Multiply the first equation with 2, the eq.1 and eq. 2 read:
2 x + 4 y + 6 z = 20 2 x + 4 y + 10 z = 20
Subtraction gives: 4 z = 0 hence z = 0.
From the first eq. we now derive x = 10 2 y . Thus the Third eq. becomes: 4 ( 10 2 y ) + y < 1 = or y > 30 7 .
Consequence: the set of solutions is given by:
{ ( 10 2 y , y , 0 ) : y > 30 7 } .
Lucian Maddox

Lucian Maddox

Expert

2022-07-02Added 8 answers

I see, thank you. My problem is my system is usually composed of M equations and N inequalities (and M+N variables) where both M and N can be very large, making an analytical solution potentially tedious

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