Mixing
Linear Programming Model with Strict Inequality and Negative Constraint
$begingroup$
I just want to know if it is possible to convert this LP model into a standard LP model:
$max Z = 2x_1+4x_2$
subject to
$-2x_1+3x_2<3$
$4x_1+5x_2>10$
$x_1 leq 0$
$x_1<4$
$x_2$ unbounded
This is my first time seeing an LP model with strict inequalities and a negative constraint. I just always see the LP model with the usual inequalities and non-negative constraint and of course, I know how to convert those LP models into standard LP models
inequality linear-programming mathematical-modeling
asked Jan 31 at 14:27
Ami78Ami78
52
$endgroup$
add a comment |
$begingroup$
I just want to know if it is possible to convert this LP model into a standard LP model:
$max Z = 2x_1+4x_2$
subject to
$-2x_1+3x_2<3$
$4x_1+5x_2>10$
$x_1 leq 0$
$x_1<4$
$x_2$ unbounded
This is my first time seeing an LP model with strict inequalities and a negative constraint. I just always see the LP model with the usual inequalities and non-negative constraint and of course, I know how to convert those LP models into standard LP models
inequality linear-programming mathematical-modeling
asked Jan 31 at 14:27
Ami78Ami78
52
$endgroup$
add a comment |
$begingroup$
I just want to know if it is possible to convert this LP model into a standard LP model:
$max Z = 2x_1+4x_2$
subject to
$-2x_1+3x_2<3$
$4x_1+5x_2>10$
$x_1 leq 0$
$x_1<4$
$x_2$ unbounded
This is my first time seeing an LP model with strict inequalities and a negative constraint. I just always see the LP model with the usual inequalities and non-negative constraint and of course, I know how to convert those LP models into standard LP models
inequality linear-programming mathematical-modeling
asked Jan 31 at 14:27
Ami78Ami78
52
$endgroup$
I just want to know if it is possible to convert this LP model into a standard LP model:
$max Z = 2x_1+4x_2$
subject to
$-2x_1+3x_2<3$
$4x_1+5x_2>10$
$x_1 leq 0$
$x_1<4$
$x_2$ unbounded
This is my first time seeing an LP model with strict inequalities and a negative constraint. I just always see the LP model with the usual inequalities and non-negative constraint and of course, I know how to convert those LP models into standard LP models
inequality linear-programming mathematical-modeling
inequality linear-programming mathematical-modeling
asked Jan 31 at 14:27
Ami78Ami78
52
asked Jan 31 at 14:27
Ami78Ami78
52
asked Jan 31 at 14:27
Ami78Ami78
52
asked Jan 31 at 14:27
Ami78Ami78
52
asked Jan 31 at 14:27
Ami78Ami78
52
52
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Replace $-2x_1+3x_2<3$ by
$$
-2x_1+3x_2 le 3-varepsilon
$$
where $varepsilon$ is a "very small" constant. And likewise for the other constraints.
answered Jan 31 at 14:30
KuifjeKuifje
7,2722726
$endgroup$
$begingroup$
Can I just use $varepsilon$ for all the other constraints? Also, what about $x_1 leq 0$?
$endgroup$
– Ami78
Jan 31 at 14:57
$begingroup$
yes you can use the same $varepsilon$ for the other constraints. For $x_1le 0$, define $hat{x}_1 = - x_1$, rewrite the constraints in terms of $hat{x}_1$, and impose $hat{x}_1 ge 0$.
$endgroup$
– Kuifje
Jan 31 at 15:40
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Replace $-2x_1+3x_2<3$ by
$$
-2x_1+3x_2 le 3-varepsilon
$$
where $varepsilon$ is a "very small" constant. And likewise for the other constraints.
answered Jan 31 at 14:30
KuifjeKuifje
7,2722726
$endgroup$
$begingroup$
Can I just use $varepsilon$ for all the other constraints? Also, what about $x_1 leq 0$?
$endgroup$
– Ami78
Jan 31 at 14:57
$begingroup$
yes you can use the same $varepsilon$ for the other constraints. For $x_1le 0$, define $hat{x}_1 = - x_1$, rewrite the constraints in terms of $hat{x}_1$, and impose $hat{x}_1 ge 0$.
$endgroup$
– Kuifje
Jan 31 at 15:40
add a comment |
$begingroup$
Replace $-2x_1+3x_2<3$ by
$$
-2x_1+3x_2 le 3-varepsilon
$$
where $varepsilon$ is a "very small" constant. And likewise for the other constraints.
answered Jan 31 at 14:30
KuifjeKuifje
7,2722726
$endgroup$
$begingroup$
Can I just use $varepsilon$ for all the other constraints? Also, what about $x_1 leq 0$?
$endgroup$
– Ami78
Jan 31 at 14:57
$begingroup$
yes you can use the same $varepsilon$ for the other constraints. For $x_1le 0$, define $hat{x}_1 = - x_1$, rewrite the constraints in terms of $hat{x}_1$, and impose $hat{x}_1 ge 0$.
$endgroup$
– Kuifje
Jan 31 at 15:40
add a comment |
$begingroup$
Replace $-2x_1+3x_2<3$ by
$$
-2x_1+3x_2 le 3-varepsilon
$$
where $varepsilon$ is a "very small" constant. And likewise for the other constraints.
answered Jan 31 at 14:30
KuifjeKuifje
7,2722726
$endgroup$
Replace $-2x_1+3x_2<3$ by
$$
-2x_1+3x_2 le 3-varepsilon
$$
where $varepsilon$ is a "very small" constant. And likewise for the other constraints.
answered Jan 31 at 14:30
KuifjeKuifje
7,2722726
answered Jan 31 at 14:30
KuifjeKuifje
7,2722726
answered Jan 31 at 14:30
KuifjeKuifje
7,2722726
answered Jan 31 at 14:30
KuifjeKuifje
7,2722726
7,2722726
$begingroup$
Can I just use $varepsilon$ for all the other constraints? Also, what about $x_1 leq 0$?
$endgroup$
– Ami78
Jan 31 at 14:57
$begingroup$
yes you can use the same $varepsilon$ for the other constraints. For $x_1le 0$, define $hat{x}_1 = - x_1$, rewrite the constraints in terms of $hat{x}_1$, and impose $hat{x}_1 ge 0$.
$endgroup$
– Kuifje
Jan 31 at 15:40
add a comment |
$begingroup$
Can I just use $varepsilon$ for all the other constraints? Also, what about $x_1 leq 0$?
$endgroup$
– Ami78
Jan 31 at 14:57
$begingroup$
yes you can use the same $varepsilon$ for the other constraints. For $x_1le 0$, define $hat{x}_1 = - x_1$, rewrite the constraints in terms of $hat{x}_1$, and impose $hat{x}_1 ge 0$.
$endgroup$
– Kuifje
Jan 31 at 15:40
$begingroup$
Can I just use $varepsilon$ for all the other constraints? Also, what about $x_1 leq 0$?
$endgroup$
– Ami78
Jan 31 at 14:57
$begingroup$
Can I just use $varepsilon$ for all the other constraints? Also, what about $x_1 leq 0$?
$endgroup$
– Ami78
Jan 31 at 14:57
$begingroup$
yes you can use the same $varepsilon$ for the other constraints. For $x_1le 0$, define $hat{x}_1 = - x_1$, rewrite the constraints in terms of $hat{x}_1$, and impose $hat{x}_1 ge 0$.
$endgroup$
– Kuifje
Jan 31 at 15:40
$begingroup$
yes you can use the same $varepsilon$ for the other constraints. For $x_1le 0$, define $hat{x}_1 = - x_1$, rewrite the constraints in terms of $hat{x}_1$, and impose $hat{x}_1 ge 0$.
$endgroup$
– Kuifje
Jan 31 at 15:40
add a comment |
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