Solve a linear problem using bounded variables method
$begingroup$
Consider the following
$$min 3x_1+4x_2\ s.t. 4x_1+3x_2ge12 \ 3x_1+4x_2le12\ x_1,x_2ge0$$
Substitute the first restriction by $x_1le3$ and solve the LP by bounded variable method.
Attempt
We first standarize and then set in a table
begin{array}{r|rrrrr|r}
& x_1 & x_2 & x_3 & x_4 & \ hline
z & -3 & -4 & 0 & 0 & & 0 \ hline
x_3 & -4 & -3 & 1 & 0 & & -12 \
x_4 & 3 & 4 & 0 & 1 & & 12
end{array}
From here we see that $theta_1=min{12/4}=3$
$theta_2=min{frac{-12-?}{-3}}=?$
and $u_2=?$
The bounded variable method requires an upper bound of $x_3$ but does not have.
How will I find $theta_2$? $u_2?$
Could someone help please?
linear-programming upper-lower-bounds operations-research
asked Dec 6 '18 at 0:52
Al t.Al t.
4291519
$endgroup$
add a comment |
$begingroup$
Consider the following
$$min 3x_1+4x_2\ s.t. 4x_1+3x_2ge12 \ 3x_1+4x_2le12\ x_1,x_2ge0$$
Substitute the first restriction by $x_1le3$ and solve the LP by bounded variable method.
Attempt
We first standarize and then set in a table
begin{array}{r|rrrrr|r}
& x_1 & x_2 & x_3 & x_4 & \ hline
z & -3 & -4 & 0 & 0 & & 0 \ hline
x_3 & -4 & -3 & 1 & 0 & & -12 \
x_4 & 3 & 4 & 0 & 1 & & 12
end{array}
From here we see that $theta_1=min{12/4}=3$
$theta_2=min{frac{-12-?}{-3}}=?$
and $u_2=?$
The bounded variable method requires an upper bound of $x_3$ but does not have.
How will I find $theta_2$? $u_2?$
Could someone help please?
linear-programming upper-lower-bounds operations-research
asked Dec 6 '18 at 0:52
Al t.Al t.
4291519
$endgroup$
add a comment |
$begingroup$
Consider the following
$$min 3x_1+4x_2\ s.t. 4x_1+3x_2ge12 \ 3x_1+4x_2le12\ x_1,x_2ge0$$
Substitute the first restriction by $x_1le3$ and solve the LP by bounded variable method.
Attempt
We first standarize and then set in a table
begin{array}{r|rrrrr|r}
& x_1 & x_2 & x_3 & x_4 & \ hline
z & -3 & -4 & 0 & 0 & & 0 \ hline
x_3 & -4 & -3 & 1 & 0 & & -12 \
x_4 & 3 & 4 & 0 & 1 & & 12
end{array}
From here we see that $theta_1=min{12/4}=3$
$theta_2=min{frac{-12-?}{-3}}=?$
and $u_2=?$
The bounded variable method requires an upper bound of $x_3$ but does not have.
How will I find $theta_2$? $u_2?$
Could someone help please?
linear-programming upper-lower-bounds operations-research
asked Dec 6 '18 at 0:52
Al t.Al t.
4291519
$endgroup$
Consider the following
$$min 3x_1+4x_2\ s.t. 4x_1+3x_2ge12 \ 3x_1+4x_2le12\ x_1,x_2ge0$$
Substitute the first restriction by $x_1le3$ and solve the LP by bounded variable method.
Attempt
We first standarize and then set in a table
begin{array}{r|rrrrr|r}
& x_1 & x_2 & x_3 & x_4 & \ hline
z & -3 & -4 & 0 & 0 & & 0 \ hline
x_3 & -4 & -3 & 1 & 0 & & -12 \
x_4 & 3 & 4 & 0 & 1 & & 12
end{array}
From here we see that $theta_1=min{12/4}=3$
$theta_2=min{frac{-12-?}{-3}}=?$
and $u_2=?$
The bounded variable method requires an upper bound of $x_3$ but does not have.
How will I find $theta_2$? $u_2?$
Could someone help please?
linear-programming upper-lower-bounds operations-research
linear-programming upper-lower-bounds operations-research
asked Dec 6 '18 at 0:52
Al t.Al t.
4291519
asked Dec 6 '18 at 0:52
Al t.Al t.
4291519
edited Dec 6 '18 at 2:06
Al t.
asked Dec 6 '18 at 0:52
Al t.Al t.
4291519
asked Dec 6 '18 at 0:52
Al t.Al t.
4291519
asked Dec 6 '18 at 0:52
Al t.Al t.
4291519
4291519
add a comment |
add a comment |
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