linprog send wrong output

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RICCARDO
RICCARDO 2024-8-29
评论： John D'Errico 2024-8-29
I'm trying ro solve linear programing problem and I'm sure of result
max 350 x1 +300 x2 +350 x3 +350x4
5 x1 + 7 x3 ≤ 119
5 x2 + 7 x4 ≤ 91
x1 + x2 ≤ 23
x3 + x4 ≤ 15
x≥0
here my command;
c=[-300 -300 -350 -350]
A=[5 0 7 0; 0 5 0 7;1 1 0 0 ; 0 0 1 1]
b =[119; 91; 23; 15]
Aeq=[]
beq=[]
lb=[0; 0; 0 ; 0]
ub=[]
linprog(c,A,b,Aeq,beq,lb,ub)
Optimal solution found.
ans =
23
0
4/7
13
right output is
24/5
91/5
95/7
0
What mistake am I making?
i tried to use the web Matlab but I got the same result.
I asked my collegue and He got the right result which the same input.

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采纳的回答

Steven Lord
Steven Lord 2024-8-29
Your objective is written mathematically as "max 350 x1 +3 x2 +3.5 x3 +3.5x4" but the c vector you've defined is "c=[-300 -300 -350 -350]".Shouldn't your c vector contain 3.5 somewhere? That seems to me to be a sign that you're not solving the problem you think you're solving.
Also you can check if your expected vector gives a larger value for the expression you're trying to maximize than the vector you believe to be the correct answer, to confirm or disprove your belief that your answer is the correct one. [Multiply -c times your vector and -c times the vector from linprog.]
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Steven Lord
Steven Lord 2024-8-29
This isn't directly about linprog but you might find this article that's somewhat related to your question interesting. It was written by Cleve Moler, chief scientist and one of the founders of MathWorks, about "impossible problems".
In it Cleve asks "I'm thinking of two numbers. Their average is 3. What are the numbers?" He shows how to compute two answers in MATLAB (one answer is 6 and 0, another is 3 and 3.) At the end, he wrote:
But three people said "2 and 4." That is certainly another "nice" answer, but the constraints it satisfies are more subtle. They have something to do with requiring the solution to have integer components that are distinct, but near the average. It's harder to state and compute in MATLAB without just giving the answer.
John D'Errico
John D'Errico 2024-8-29
Ran in:
In the simple example @Steven Lord gives, where the mean of two numbers is known, the solution can be written as
[3 - t, 3 + t]
where any value for t will generate the same mean, yet a completely different, and equally valid result.
How about the question posed in the linear program? Are they both valid solutions? (Now that the equations have been correctly written.)
c=[-300 -300 -350 -350];
A=[5 0 7 0; 0 5 0 7;1 1 0 0 ; 0 0 1 1];
b =[119; 91; 23; 15];
x1 = [23;0;4/7;13];
x2 = [24/5;91/5;95/7;0];
A*x1 <= b
ans = 4x1 logical array
1 1 1 1
A*x2 <= b
ans = 4x1 logical array
1 1 1 1
c*x1
ans = -11650
c*x2
ans = -11650
Both return the same solution, so both are equally valid. We might decide to find a more general family of solutions, given x1 and x2.
dx = x2 - x1
dx = 4x1
-18.2000 18.2000 13.0000 -13.0000
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syms t
xgeneral = x1 + dx*t
xgeneral = 
c*xgeneral
ans = 
Again, the objective is unchanged, for any value of t.
A*xgeneral <= b
ans = 
As well, we see the inequality constraints are satisfied for all values of t. Although the 4th inequality constraint is never apparently active.
It is likely that the bound constraints will not always be satisfied. As long as t lies between 0 and 1, then the bound constraints wil be satisfied.
So what do we see happening here? The first three constraints can be visualized as forming a line in the 4 dimensional parameter space. AND that line just happens to be orthogonal to the objective function. So any point along that line will be a solution.

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