How to run please this example perfectly to get optimal solution .. Thank you

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Dalia ElNakib 2023-5-4

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https://ww2.mathworks.cn/matlabcentral/answers/1958024-how-to-run-please-this-example-perfectly-to-get-optimal-solution-thank-you

评论： Dalia ElNakib 2023-5-6

f = [0 ; - 10 ; 0 ; - 6; - 20] ; 
A = [1 0 0 0 0 ;
     0 1 0 0 0 ;
     0 0 1 0 0 ;
     0 0 0 1 0 ;
     0 0 0 0 1] ;
B = [4 ; 3 ; 3 ; 2 ; 2] ; 
Aeq = [1 - 1 - 1 0 0 ; 0 0 1 - 1 - 1] ;
beq = [0; 0; 0; 0; 0]; 
lb = zeros (5, 1) ;
ub = zeros (5, 1) ;
x = linprog(f,A,B,Aeq,beq,lb,ub)
[x,fval] = linprog(f,A,Aeq,beq,lb,ub);

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Answer 1

Steven Lord 2023-5-4

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lb = zeros (5, 1) ;
ub = zeros (5, 1) ;

So based on the way you've constructed the bounds, all the elements of your solution have to be greater than or equal to 0 and less than or equal to 0. The only possible solution that satisfies both sets of bounds is zeros(5, 1).

Are you sure that ub shouldn't be something like ones(5, 1)?

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Steven Lord 2023-5-4

Yes, I saw that. I would have expected them also to appear in the "Therefore, the problem can be posed as the following linear program:" section as inequalities like the last three bound constraints. But due to a lack of space on the page I wonder if students solving the problem could overlook the last two equations (which I assumed appeared after the diagram on page 262.)

Dalia ElNakib 2023-5-6

Many Thanks for your clarifications.

Really appreciate your efforts.

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Answer 2

Torsten 2023-5-4

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https://ww2.mathworks.cn/matlabcentral/answers/1958024-how-to-run-please-this-example-perfectly-to-get-optimal-solution-thank-you#answer_1229134

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f = [0 ; -10 ; 0 ; -6; -20] ; 
A = [1 0 0 0 0 ;
     0 1 0 0 0 ;
     0 0 1 0 0 ;
     0 0 0 1 0 ;
     0 0 0 0 1] ;
B = [4 ; 3 ; 3 ; 2 ; 2] ; 
Aeq = [1 -1 -1 0 0 ; 0 0 1 -1 -1] ;
beq = [0; 0]; 
lb = zeros (5, 1) ;
ub = zeros (5, 1) ;
[x,fval] = linprog(f,A,B,Aeq,beq,lb,ub)
Optimal solution found.
x = 5×1
     0
     0
     0
     0
     0
fval = 0

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Dalia ElNakib 2023-5-4

在 MATLAB Online 中打开

f = [0 ; -10 ; 0 ; -6; -20] ; 
A = [1 0 0 0 0 ;
     0 1 0 0 0 ;
     0 0 1 0 0 ;
     0 0 0 1 0 ;
     0 0 0 0 1] ;
B = [4 ; 3 ; 3 ; 2 ; 2] ; 
Aeq = [1 -1 -1 0 0 ; 0 0 1 -1 -1] ;
beq = [0; 0]; 
lb = zeros (5, 1) ;
ub = ones(5, 1);
[x,fval] = linprog(f,A,B,Aeq,beq,lb,ub);
Optimal solution found.

Dalia ElNakib 2023-5-4

编辑：Dalia ElNakib 2023-5-4

在 MATLAB Online 中打开

@Torsten @Steven Lord

Thank you so much

Both work to ge the optimal solution

Either:

lb = zeros (5, 1) ;

ub = zeros (5, 1) ;

Or

lb = zeros (5, 1) ;

ub = ones (5, 1) ;

f = [0 ; -10 ; 0 ; -6; -20] ; 
A = [1 0 0 0 0 ;
     0 1 0 0 0 ;
     0 0 1 0 0 ;
     0 0 0 1 0 ;
     0 0 0 0 1] ;
B = [4 ; 3 ; 3 ; 2 ; 2] ; 
Aeq = [1 -1 -1 0 0 ; 0 0 1 -1 -1] ;
beq = [0; 0]; 
lb = zeros (5, 1) ;
ub = zeros(5, 1);
[x,fval] = linprog(f,A,B,Aeq,beq,lb,ub);
Optimal solution found.