Solving an LP problem with an upper limit for the variables
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Im trying to solve the Above LP. Now, can we apply just simplex considering that we can treat the upper bounds of the variables as constraints.
Meaning, we need to add $6$ slack variables, and it would be a bit harder to do the algorithm by hand. Now, the dual will give six variables as well, so it doesnt help much.
In my notes, it says to consider "bounded variable simplex method", but I haven't seen how this method works. how can we apply this method to solve this problem? Is it possible to solve it using the standard primal simplex?
linear-programming
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Im trying to solve the Above LP. Now, can we apply just simplex considering that we can treat the upper bounds of the variables as constraints.
Meaning, we need to add $6$ slack variables, and it would be a bit harder to do the algorithm by hand. Now, the dual will give six variables as well, so it doesnt help much.
In my notes, it says to consider "bounded variable simplex method", but I haven't seen how this method works. how can we apply this method to solve this problem? Is it possible to solve it using the standard primal simplex?
linear-programming
1
Here is a algorithm for Bounded Variables with examples.
– callculus
Nov 16 at 12:24
What more do you expect from an answer than the algorithm callculus linked to?
– LinAlg
Nov 18 at 13:57
LinAlg The example in the link is different than my problem. I dont see a way to apply what is on this link to this actual problem.
– Jimmy Sabater
Nov 19 at 7:51
Could you add to your question where you get stuck? The examples on pages 5-8 seem to cover your needs.
– LinAlg
Nov 19 at 14:28
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Im trying to solve the Above LP. Now, can we apply just simplex considering that we can treat the upper bounds of the variables as constraints.
Meaning, we need to add $6$ slack variables, and it would be a bit harder to do the algorithm by hand. Now, the dual will give six variables as well, so it doesnt help much.
In my notes, it says to consider "bounded variable simplex method", but I haven't seen how this method works. how can we apply this method to solve this problem? Is it possible to solve it using the standard primal simplex?
linear-programming
Im trying to solve the Above LP. Now, can we apply just simplex considering that we can treat the upper bounds of the variables as constraints.
Meaning, we need to add $6$ slack variables, and it would be a bit harder to do the algorithm by hand. Now, the dual will give six variables as well, so it doesnt help much.
In my notes, it says to consider "bounded variable simplex method", but I haven't seen how this method works. how can we apply this method to solve this problem? Is it possible to solve it using the standard primal simplex?
linear-programming
linear-programming
asked Nov 16 at 7:11
Jimmy Sabater
1,831218
1,831218
1
Here is a algorithm for Bounded Variables with examples.
– callculus
Nov 16 at 12:24
What more do you expect from an answer than the algorithm callculus linked to?
– LinAlg
Nov 18 at 13:57
LinAlg The example in the link is different than my problem. I dont see a way to apply what is on this link to this actual problem.
– Jimmy Sabater
Nov 19 at 7:51
Could you add to your question where you get stuck? The examples on pages 5-8 seem to cover your needs.
– LinAlg
Nov 19 at 14:28
add a comment |
1
Here is a algorithm for Bounded Variables with examples.
– callculus
Nov 16 at 12:24
What more do you expect from an answer than the algorithm callculus linked to?
– LinAlg
Nov 18 at 13:57
LinAlg The example in the link is different than my problem. I dont see a way to apply what is on this link to this actual problem.
– Jimmy Sabater
Nov 19 at 7:51
Could you add to your question where you get stuck? The examples on pages 5-8 seem to cover your needs.
– LinAlg
Nov 19 at 14:28
1
1
Here is a algorithm for Bounded Variables with examples.
– callculus
Nov 16 at 12:24
Here is a algorithm for Bounded Variables with examples.
– callculus
Nov 16 at 12:24
What more do you expect from an answer than the algorithm callculus linked to?
– LinAlg
Nov 18 at 13:57
What more do you expect from an answer than the algorithm callculus linked to?
– LinAlg
Nov 18 at 13:57
LinAlg The example in the link is different than my problem. I dont see a way to apply what is on this link to this actual problem.
– Jimmy Sabater
Nov 19 at 7:51
LinAlg The example in the link is different than my problem. I dont see a way to apply what is on this link to this actual problem.
– Jimmy Sabater
Nov 19 at 7:51
Could you add to your question where you get stuck? The examples on pages 5-8 seem to cover your needs.
– LinAlg
Nov 19 at 14:28
Could you add to your question where you get stuck? The examples on pages 5-8 seem to cover your needs.
– LinAlg
Nov 19 at 14:28
add a comment |
1 Answer
1
active
oldest
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up vote
4
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accepted
Let's write down our simplex table, remembering our upper bounds for each variables.
begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}hline
& x_1 & x_2 & x_3 & x_4 & x_5 & s & -z & RHS & text{ratio} &UB \ hline
-z & -2 & -4 & color{blue}{-7} & -1 & -5 & 0 & 1 & 0 & - & - \ hline
s & 3 & 5 & 11 & 2 & 7 & 1 & 0 & 10 & frac{10}{11} & 1 \ hline
end{array}
At the beginning, we are at $(x_1,x_2,x_3,x_4,x_5)=(0,0,0,0,0)$. The entering variable would be $x_3$. since the minimum ratio is less than the upper bound, we will do a regular simplex pivot updating.
begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}hline
& x_1 & x_2 & x_3 & x_4 & x_5 & s & -z & RHS & text{ratio} &UB \ hline
-z & -frac1{11} & color{blue}{-frac9{11}} & 0 & frac3{11} & -frac6{11} & frac7{11} & 1 & frac{70}{11} & - & - \ hline
x_3 & frac3{11} & frac5{11} & 1 & frac2{11} & frac7{11} & frac1{11} & 0 & frac{10}{11} & 2 & 1 \ hline
end{array}
Upon doing the simplex update, we reach $(0,0,frac{10}{11},0,0)$. Our next entering variable is $x_2$. The difference from the previous step this time is the ratio is more than the upper bound. We will increment the $x_2$ by the upperbound amount, which is $1$. We will also update the RHS and mark $x_2$ as $bar{x}_2$ to indicate that it is now non-basic.
begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}hline
& x_1 & bar{x}_2 & x_3 & x_4 & x_5 & s & -z & RHS & text{ratio} &UB \ hline
-z & -frac1{11} & -frac9{11} & 0 & frac3{11} & color{blue}{-frac6{11}} & frac7{11} & 1 & frac{79}{11} & - & - \ hline
x_3 & frac3{11} & frac5{11} & 1 & frac2{11} & frac7{11} & frac1{11} & 0 & frac{5}{11} & frac57 & 1 \ hline
end{array}
Now, we arrive at $(0,1,frac5{11},0,0)$. Our next entering variable is $x_5$, since the ratio is less than the upper bound, we do a regular simplex pivot updating.
begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}hline
& x_1 & bar{x}_2 & x_3 & x_4 & x_5 & s & -z & RHS & text{ratio} &UB \ hline
-z & frac1{7} & -frac3{7} & frac67 & frac3{7} & 0 & frac5{7} & 1 & frac{53}{7} & - & - \ hline
x_5 & frac3{7} & frac5{7} & frac{11}7 & frac2{7} & 1 & frac1{7} & 0 & frac{5}{7} & - & - \ hline
end{array}
Now, we arrive at $(0,1,0,0,frac57)$. Upon checking the reduced cost, we can see that we are optimal with objective value $frac{53}{7}$.
R code to check the final solution:
> library(lpSolve)
> f.obj <- c(2,4,7,1,5)
> n = length(f.obj)
> f.con <- rbind(c(3,5,11,2,7), diag(n), -diag(n))
> f.dir <- rep('<=',2 * n+1 )
> f.rhs <- c(10,rep(1,n),rep(0,n))
> optimum <- lp(direction = "max", objective.in = f.obj, const.mat = f.con, const.dir = f.dir, const.rhs = f.rhs)
> optimum
Success: the objective function is 7.571429
> optimum$solution
[1] 0.0000000 1.0000000 0.0000000 0.0000000 0.7142857
its very nice, thanks so much! I have a question though. At the beginning, you decide it to put all $x_i$ at $0$, which it at their lower bound. I assume this choice is arbitrary. You could have choosen say $x_1=x_2=1$ and the rest $0$ and this would still work, correct?
– Jimmy Sabater
Nov 22 at 2:26
Sure, just adjust accodingly.
– Siong Thye Goh
Nov 22 at 3:16
Can you help me with this question? math.stackexchange.com/questions/3007305/…
– Jimmy Sabater
Nov 22 at 4:41
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
4
down vote
accepted
Let's write down our simplex table, remembering our upper bounds for each variables.
begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}hline
& x_1 & x_2 & x_3 & x_4 & x_5 & s & -z & RHS & text{ratio} &UB \ hline
-z & -2 & -4 & color{blue}{-7} & -1 & -5 & 0 & 1 & 0 & - & - \ hline
s & 3 & 5 & 11 & 2 & 7 & 1 & 0 & 10 & frac{10}{11} & 1 \ hline
end{array}
At the beginning, we are at $(x_1,x_2,x_3,x_4,x_5)=(0,0,0,0,0)$. The entering variable would be $x_3$. since the minimum ratio is less than the upper bound, we will do a regular simplex pivot updating.
begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}hline
& x_1 & x_2 & x_3 & x_4 & x_5 & s & -z & RHS & text{ratio} &UB \ hline
-z & -frac1{11} & color{blue}{-frac9{11}} & 0 & frac3{11} & -frac6{11} & frac7{11} & 1 & frac{70}{11} & - & - \ hline
x_3 & frac3{11} & frac5{11} & 1 & frac2{11} & frac7{11} & frac1{11} & 0 & frac{10}{11} & 2 & 1 \ hline
end{array}
Upon doing the simplex update, we reach $(0,0,frac{10}{11},0,0)$. Our next entering variable is $x_2$. The difference from the previous step this time is the ratio is more than the upper bound. We will increment the $x_2$ by the upperbound amount, which is $1$. We will also update the RHS and mark $x_2$ as $bar{x}_2$ to indicate that it is now non-basic.
begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}hline
& x_1 & bar{x}_2 & x_3 & x_4 & x_5 & s & -z & RHS & text{ratio} &UB \ hline
-z & -frac1{11} & -frac9{11} & 0 & frac3{11} & color{blue}{-frac6{11}} & frac7{11} & 1 & frac{79}{11} & - & - \ hline
x_3 & frac3{11} & frac5{11} & 1 & frac2{11} & frac7{11} & frac1{11} & 0 & frac{5}{11} & frac57 & 1 \ hline
end{array}
Now, we arrive at $(0,1,frac5{11},0,0)$. Our next entering variable is $x_5$, since the ratio is less than the upper bound, we do a regular simplex pivot updating.
begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}hline
& x_1 & bar{x}_2 & x_3 & x_4 & x_5 & s & -z & RHS & text{ratio} &UB \ hline
-z & frac1{7} & -frac3{7} & frac67 & frac3{7} & 0 & frac5{7} & 1 & frac{53}{7} & - & - \ hline
x_5 & frac3{7} & frac5{7} & frac{11}7 & frac2{7} & 1 & frac1{7} & 0 & frac{5}{7} & - & - \ hline
end{array}
Now, we arrive at $(0,1,0,0,frac57)$. Upon checking the reduced cost, we can see that we are optimal with objective value $frac{53}{7}$.
R code to check the final solution:
> library(lpSolve)
> f.obj <- c(2,4,7,1,5)
> n = length(f.obj)
> f.con <- rbind(c(3,5,11,2,7), diag(n), -diag(n))
> f.dir <- rep('<=',2 * n+1 )
> f.rhs <- c(10,rep(1,n),rep(0,n))
> optimum <- lp(direction = "max", objective.in = f.obj, const.mat = f.con, const.dir = f.dir, const.rhs = f.rhs)
> optimum
Success: the objective function is 7.571429
> optimum$solution
[1] 0.0000000 1.0000000 0.0000000 0.0000000 0.7142857
its very nice, thanks so much! I have a question though. At the beginning, you decide it to put all $x_i$ at $0$, which it at their lower bound. I assume this choice is arbitrary. You could have choosen say $x_1=x_2=1$ and the rest $0$ and this would still work, correct?
– Jimmy Sabater
Nov 22 at 2:26
Sure, just adjust accodingly.
– Siong Thye Goh
Nov 22 at 3:16
Can you help me with this question? math.stackexchange.com/questions/3007305/…
– Jimmy Sabater
Nov 22 at 4:41
add a comment |
up vote
4
down vote
accepted
Let's write down our simplex table, remembering our upper bounds for each variables.
begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}hline
& x_1 & x_2 & x_3 & x_4 & x_5 & s & -z & RHS & text{ratio} &UB \ hline
-z & -2 & -4 & color{blue}{-7} & -1 & -5 & 0 & 1 & 0 & - & - \ hline
s & 3 & 5 & 11 & 2 & 7 & 1 & 0 & 10 & frac{10}{11} & 1 \ hline
end{array}
At the beginning, we are at $(x_1,x_2,x_3,x_4,x_5)=(0,0,0,0,0)$. The entering variable would be $x_3$. since the minimum ratio is less than the upper bound, we will do a regular simplex pivot updating.
begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}hline
& x_1 & x_2 & x_3 & x_4 & x_5 & s & -z & RHS & text{ratio} &UB \ hline
-z & -frac1{11} & color{blue}{-frac9{11}} & 0 & frac3{11} & -frac6{11} & frac7{11} & 1 & frac{70}{11} & - & - \ hline
x_3 & frac3{11} & frac5{11} & 1 & frac2{11} & frac7{11} & frac1{11} & 0 & frac{10}{11} & 2 & 1 \ hline
end{array}
Upon doing the simplex update, we reach $(0,0,frac{10}{11},0,0)$. Our next entering variable is $x_2$. The difference from the previous step this time is the ratio is more than the upper bound. We will increment the $x_2$ by the upperbound amount, which is $1$. We will also update the RHS and mark $x_2$ as $bar{x}_2$ to indicate that it is now non-basic.
begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}hline
& x_1 & bar{x}_2 & x_3 & x_4 & x_5 & s & -z & RHS & text{ratio} &UB \ hline
-z & -frac1{11} & -frac9{11} & 0 & frac3{11} & color{blue}{-frac6{11}} & frac7{11} & 1 & frac{79}{11} & - & - \ hline
x_3 & frac3{11} & frac5{11} & 1 & frac2{11} & frac7{11} & frac1{11} & 0 & frac{5}{11} & frac57 & 1 \ hline
end{array}
Now, we arrive at $(0,1,frac5{11},0,0)$. Our next entering variable is $x_5$, since the ratio is less than the upper bound, we do a regular simplex pivot updating.
begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}hline
& x_1 & bar{x}_2 & x_3 & x_4 & x_5 & s & -z & RHS & text{ratio} &UB \ hline
-z & frac1{7} & -frac3{7} & frac67 & frac3{7} & 0 & frac5{7} & 1 & frac{53}{7} & - & - \ hline
x_5 & frac3{7} & frac5{7} & frac{11}7 & frac2{7} & 1 & frac1{7} & 0 & frac{5}{7} & - & - \ hline
end{array}
Now, we arrive at $(0,1,0,0,frac57)$. Upon checking the reduced cost, we can see that we are optimal with objective value $frac{53}{7}$.
R code to check the final solution:
> library(lpSolve)
> f.obj <- c(2,4,7,1,5)
> n = length(f.obj)
> f.con <- rbind(c(3,5,11,2,7), diag(n), -diag(n))
> f.dir <- rep('<=',2 * n+1 )
> f.rhs <- c(10,rep(1,n),rep(0,n))
> optimum <- lp(direction = "max", objective.in = f.obj, const.mat = f.con, const.dir = f.dir, const.rhs = f.rhs)
> optimum
Success: the objective function is 7.571429
> optimum$solution
[1] 0.0000000 1.0000000 0.0000000 0.0000000 0.7142857
its very nice, thanks so much! I have a question though. At the beginning, you decide it to put all $x_i$ at $0$, which it at their lower bound. I assume this choice is arbitrary. You could have choosen say $x_1=x_2=1$ and the rest $0$ and this would still work, correct?
– Jimmy Sabater
Nov 22 at 2:26
Sure, just adjust accodingly.
– Siong Thye Goh
Nov 22 at 3:16
Can you help me with this question? math.stackexchange.com/questions/3007305/…
– Jimmy Sabater
Nov 22 at 4:41
add a comment |
up vote
4
down vote
accepted
up vote
4
down vote
accepted
Let's write down our simplex table, remembering our upper bounds for each variables.
begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}hline
& x_1 & x_2 & x_3 & x_4 & x_5 & s & -z & RHS & text{ratio} &UB \ hline
-z & -2 & -4 & color{blue}{-7} & -1 & -5 & 0 & 1 & 0 & - & - \ hline
s & 3 & 5 & 11 & 2 & 7 & 1 & 0 & 10 & frac{10}{11} & 1 \ hline
end{array}
At the beginning, we are at $(x_1,x_2,x_3,x_4,x_5)=(0,0,0,0,0)$. The entering variable would be $x_3$. since the minimum ratio is less than the upper bound, we will do a regular simplex pivot updating.
begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}hline
& x_1 & x_2 & x_3 & x_4 & x_5 & s & -z & RHS & text{ratio} &UB \ hline
-z & -frac1{11} & color{blue}{-frac9{11}} & 0 & frac3{11} & -frac6{11} & frac7{11} & 1 & frac{70}{11} & - & - \ hline
x_3 & frac3{11} & frac5{11} & 1 & frac2{11} & frac7{11} & frac1{11} & 0 & frac{10}{11} & 2 & 1 \ hline
end{array}
Upon doing the simplex update, we reach $(0,0,frac{10}{11},0,0)$. Our next entering variable is $x_2$. The difference from the previous step this time is the ratio is more than the upper bound. We will increment the $x_2$ by the upperbound amount, which is $1$. We will also update the RHS and mark $x_2$ as $bar{x}_2$ to indicate that it is now non-basic.
begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}hline
& x_1 & bar{x}_2 & x_3 & x_4 & x_5 & s & -z & RHS & text{ratio} &UB \ hline
-z & -frac1{11} & -frac9{11} & 0 & frac3{11} & color{blue}{-frac6{11}} & frac7{11} & 1 & frac{79}{11} & - & - \ hline
x_3 & frac3{11} & frac5{11} & 1 & frac2{11} & frac7{11} & frac1{11} & 0 & frac{5}{11} & frac57 & 1 \ hline
end{array}
Now, we arrive at $(0,1,frac5{11},0,0)$. Our next entering variable is $x_5$, since the ratio is less than the upper bound, we do a regular simplex pivot updating.
begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}hline
& x_1 & bar{x}_2 & x_3 & x_4 & x_5 & s & -z & RHS & text{ratio} &UB \ hline
-z & frac1{7} & -frac3{7} & frac67 & frac3{7} & 0 & frac5{7} & 1 & frac{53}{7} & - & - \ hline
x_5 & frac3{7} & frac5{7} & frac{11}7 & frac2{7} & 1 & frac1{7} & 0 & frac{5}{7} & - & - \ hline
end{array}
Now, we arrive at $(0,1,0,0,frac57)$. Upon checking the reduced cost, we can see that we are optimal with objective value $frac{53}{7}$.
R code to check the final solution:
> library(lpSolve)
> f.obj <- c(2,4,7,1,5)
> n = length(f.obj)
> f.con <- rbind(c(3,5,11,2,7), diag(n), -diag(n))
> f.dir <- rep('<=',2 * n+1 )
> f.rhs <- c(10,rep(1,n),rep(0,n))
> optimum <- lp(direction = "max", objective.in = f.obj, const.mat = f.con, const.dir = f.dir, const.rhs = f.rhs)
> optimum
Success: the objective function is 7.571429
> optimum$solution
[1] 0.0000000 1.0000000 0.0000000 0.0000000 0.7142857
Let's write down our simplex table, remembering our upper bounds for each variables.
begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}hline
& x_1 & x_2 & x_3 & x_4 & x_5 & s & -z & RHS & text{ratio} &UB \ hline
-z & -2 & -4 & color{blue}{-7} & -1 & -5 & 0 & 1 & 0 & - & - \ hline
s & 3 & 5 & 11 & 2 & 7 & 1 & 0 & 10 & frac{10}{11} & 1 \ hline
end{array}
At the beginning, we are at $(x_1,x_2,x_3,x_4,x_5)=(0,0,0,0,0)$. The entering variable would be $x_3$. since the minimum ratio is less than the upper bound, we will do a regular simplex pivot updating.
begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}hline
& x_1 & x_2 & x_3 & x_4 & x_5 & s & -z & RHS & text{ratio} &UB \ hline
-z & -frac1{11} & color{blue}{-frac9{11}} & 0 & frac3{11} & -frac6{11} & frac7{11} & 1 & frac{70}{11} & - & - \ hline
x_3 & frac3{11} & frac5{11} & 1 & frac2{11} & frac7{11} & frac1{11} & 0 & frac{10}{11} & 2 & 1 \ hline
end{array}
Upon doing the simplex update, we reach $(0,0,frac{10}{11},0,0)$. Our next entering variable is $x_2$. The difference from the previous step this time is the ratio is more than the upper bound. We will increment the $x_2$ by the upperbound amount, which is $1$. We will also update the RHS and mark $x_2$ as $bar{x}_2$ to indicate that it is now non-basic.
begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}hline
& x_1 & bar{x}_2 & x_3 & x_4 & x_5 & s & -z & RHS & text{ratio} &UB \ hline
-z & -frac1{11} & -frac9{11} & 0 & frac3{11} & color{blue}{-frac6{11}} & frac7{11} & 1 & frac{79}{11} & - & - \ hline
x_3 & frac3{11} & frac5{11} & 1 & frac2{11} & frac7{11} & frac1{11} & 0 & frac{5}{11} & frac57 & 1 \ hline
end{array}
Now, we arrive at $(0,1,frac5{11},0,0)$. Our next entering variable is $x_5$, since the ratio is less than the upper bound, we do a regular simplex pivot updating.
begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}hline
& x_1 & bar{x}_2 & x_3 & x_4 & x_5 & s & -z & RHS & text{ratio} &UB \ hline
-z & frac1{7} & -frac3{7} & frac67 & frac3{7} & 0 & frac5{7} & 1 & frac{53}{7} & - & - \ hline
x_5 & frac3{7} & frac5{7} & frac{11}7 & frac2{7} & 1 & frac1{7} & 0 & frac{5}{7} & - & - \ hline
end{array}
Now, we arrive at $(0,1,0,0,frac57)$. Upon checking the reduced cost, we can see that we are optimal with objective value $frac{53}{7}$.
R code to check the final solution:
> library(lpSolve)
> f.obj <- c(2,4,7,1,5)
> n = length(f.obj)
> f.con <- rbind(c(3,5,11,2,7), diag(n), -diag(n))
> f.dir <- rep('<=',2 * n+1 )
> f.rhs <- c(10,rep(1,n),rep(0,n))
> optimum <- lp(direction = "max", objective.in = f.obj, const.mat = f.con, const.dir = f.dir, const.rhs = f.rhs)
> optimum
Success: the objective function is 7.571429
> optimum$solution
[1] 0.0000000 1.0000000 0.0000000 0.0000000 0.7142857
edited Nov 19 at 17:53
answered Nov 19 at 17:36
Siong Thye Goh
94.9k1462115
94.9k1462115
its very nice, thanks so much! I have a question though. At the beginning, you decide it to put all $x_i$ at $0$, which it at their lower bound. I assume this choice is arbitrary. You could have choosen say $x_1=x_2=1$ and the rest $0$ and this would still work, correct?
– Jimmy Sabater
Nov 22 at 2:26
Sure, just adjust accodingly.
– Siong Thye Goh
Nov 22 at 3:16
Can you help me with this question? math.stackexchange.com/questions/3007305/…
– Jimmy Sabater
Nov 22 at 4:41
add a comment |
its very nice, thanks so much! I have a question though. At the beginning, you decide it to put all $x_i$ at $0$, which it at their lower bound. I assume this choice is arbitrary. You could have choosen say $x_1=x_2=1$ and the rest $0$ and this would still work, correct?
– Jimmy Sabater
Nov 22 at 2:26
Sure, just adjust accodingly.
– Siong Thye Goh
Nov 22 at 3:16
Can you help me with this question? math.stackexchange.com/questions/3007305/…
– Jimmy Sabater
Nov 22 at 4:41
its very nice, thanks so much! I have a question though. At the beginning, you decide it to put all $x_i$ at $0$, which it at their lower bound. I assume this choice is arbitrary. You could have choosen say $x_1=x_2=1$ and the rest $0$ and this would still work, correct?
– Jimmy Sabater
Nov 22 at 2:26
its very nice, thanks so much! I have a question though. At the beginning, you decide it to put all $x_i$ at $0$, which it at their lower bound. I assume this choice is arbitrary. You could have choosen say $x_1=x_2=1$ and the rest $0$ and this would still work, correct?
– Jimmy Sabater
Nov 22 at 2:26
Sure, just adjust accodingly.
– Siong Thye Goh
Nov 22 at 3:16
Sure, just adjust accodingly.
– Siong Thye Goh
Nov 22 at 3:16
Can you help me with this question? math.stackexchange.com/questions/3007305/…
– Jimmy Sabater
Nov 22 at 4:41
Can you help me with this question? math.stackexchange.com/questions/3007305/…
– Jimmy Sabater
Nov 22 at 4:41
add a comment |
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1
Here is a algorithm for Bounded Variables with examples.
– callculus
Nov 16 at 12:24
What more do you expect from an answer than the algorithm callculus linked to?
– LinAlg
Nov 18 at 13:57
LinAlg The example in the link is different than my problem. I dont see a way to apply what is on this link to this actual problem.
– Jimmy Sabater
Nov 19 at 7:51
Could you add to your question where you get stuck? The examples on pages 5-8 seem to cover your needs.
– LinAlg
Nov 19 at 14:28