Linear Programming In C#

Question

Hello everybody, i need your help to solve this in c#:

X14 + X24 + X34 + 30 lambda = 130
X14 + X24 + X34 - 10 lambda = 90
X14 + X23 + X33 + 10 lambda = 100
X14 + X23 + X33 - 20 lambda = 70
X13 + X23 + X32 + 15 lambda = 95
X13 + X23 + X32 - 10 lambda = 70
X12 + X22 + X31 + 10 lambda = 80
X12 + X22 + X31 - 10 lambda = 60
X12 + X21 + X32 + 5 lambda = 65
X12 + X21 + X32 - 10 lambda = 60
X11 + X21 + X31 = 60
X14 + X24 + X34 = 150
X12 - X11 = 4
X13 - X12 = 4
X14 - X13 = 4
X22 - X21 = 4
X23 - X22 = 4
X24 - X23 = 4
X32 - X31 = 4
X33 - X32 = 4
X34 - X33 = 4
Xij = 0 (i = 1,2, ... , m ; j = 1,2, ... , n)

How do i solve this problem in c# winforms ?
i am confused, how i can get the answer /value for each data ( lambda , x11, x12, 13, etc )

Please help me.
Thank you.
Have a great day. :)

Vulpes · Answer

What I'm saying, Nico, is that your application needs some sort of settings file which it loads before doing anything else. This file needs to contain: The value of i The value of j The value of each Xij The maximum salary value So after loading this file, you'd have these variables - I'm initializing them manually for illustration but in practice, of course, you'd get them from the file: const int i = 3; const int j = 4; double[,] x = new double[i,j] { {52.4, 56.4, 60.4, 66}, {0, 12.8, 16.8, 21.6}, {0, 4, 8, 12} }; double maxSalary = 100000; So you can now work out the maximum number of points by adding up the figures in the final column: double maxPoints = 0; for(int k = 0; k { maxPoints += x[k, j - 1]; } which, on the figures used gives 99.6 and this then corresponds to the maxSalary of 100,000. The salaries of other individuals can then be deduced from their scores by simple proportion.

Nico Darmawan · Answer

What I'm saying, Nico, is that your application needs some sort of settings file which it loads before doing anything else. This file needs to contain: The value of i The value of j The value of each Xij The maximum salary value Finally i got it. So i must count the value of each Xij manually on the paper and then declare it in the program. So for now it's impossible to customize the application, it means that for now i = 3, j = 4 It's because i can't count the value of each Xij, so i just rely on the value contained in the book. Thank you so much for your help, patience and opinion. God bless you. :)

Nico Darmawan · Answer

To Mr Vulpes If you increased i or j, then the calculations would need to be revised but it's not difficult to allow for all this. I am still dont get the idea for yours (above) sentences. Revised? You mean i must presuppose the value based on the current standard value? A bit confuse how to do the calculations. Do you mind to explain it sir? Thank you very much.

Vulpes · Answer

If you keep all the Xij constant, then the only variable is how much salary is the highest score of 99.6 equivalent to. If it's equivalent to 100,000 one year then it might be equivalent to 103,000 the next year if there's 3% salary inflation. You could set this value in a text or XML file and change it as needed. You could also keep the Xij in the file and change them if it becomes clear that the weightings are no longer appropriate. The highest score will always be X14 + X24 + X34 so if this increased (say) to 105, then the highest salary in the settings file would now be equivalent to a score of 105 rather than 99.6. If you increased i or j, then the calculations would need to be revised but it's not difficult to allow for all this.

Nico Darmawan · Answer

To Mr Vurpes It's very simple if i just use the answer from the book, save it into an array / db, access them according what i need in the future. But what if the factor become 4 not 3? or each factor have more type: x11,x12,x13,x14,x15 Do you have any suggestion or idea? Please tell me if you have in your mind sir. Thank you Mr Vurpes for all your attention until now. :)

Vulpes · Answer

Do you actually need to solve any equations here? Could you just use the answers in the book, which look reasonable to me, if they're based on some 'real life' study and then correlate them with some actual salaries? For example, suppose you have a person who has the attributes: X14 + X24 + X34 which have a score of 66 + 21.6 + 12 = 99.6 and this person earns a salary of 100,000 (units of some currency). If you then had another person with the attributes: X11 + X21 + X31 which have a score of 52.4 + 0 + 0 = 52.4 you could argue (if the relationship between salary and scores is linear) that the second person should receive a salary of: 52.4 / 99.6 x 100000 = 52,610 say 52,000. To build an application on these lines would be very easy.

Nico Darmawan · Answer

So its impossible huh? T.T i got crazy after read your reply cause i don't know what to do now. I would like to make an salary application. Explanation : During this payroll employees in a company are often made ??with provisions that are firm . For example : payment of salaries based on years of service , or based on class , or education . Yet in reality there are many other factors that influence , such as the severity of a job or responsibility that must be borne employees in carrying out his job . Factors - factors like these is quite difficult if it has to be identified unequivocally . An employee who has a low complexity of work should earn a lower salary compared to a high complexity . As well as employees who work without supervision should receive higher salaries compared to that get full control . The size of heavy / light or a lot / a little of this oversight is not expressly or vague ( fuzzy). I choose 3 major factor that can be used to evaluate the job : 1. complexity of the work 2. the need for supervision 3. physical endurance Each factor divide to 4 level : Factor 1 : complexity of the work x11 = low x12 = intermediate x13 = high enough x14 = high Factor 2 : the need for supervision x21 = really need x22 = need x23 = little need x24 = no need Factor 3 : physical endurance x31 = no need x32 = little need x33 = need x34 = very need What do you think of these idea? So it is impossible to make this application? I am so dizzy right now. Do you have any recommendation or do you have ever make an application like this or do you know any blog about this? Sorry if my english is bad (i used translate.google). As a junior, i need your advice sir. Thank you for everything until now. :)

Vulpes · Answer

Well, that makes more sense than it did but the answers they give (or some of them) can't be correct. If we forget about the lambda parts and just evaluate the last 10 'exact' expressions using the purported answers we get: X11 + X21 + X31 = 52.4 (not 60) X14 + X24 + X34 = 99.6 (not 150) X12 - X11 = 4 (correct) X13 - X12 = 4 (correct) X14 - X13 = 5.6 (not 4) X22 - X21 = 12.8 (not 4) X23 - X22 = 4 (correct) X24 - X23 = 4.8 (not 4) X32 - X31 = 4 (correct) X33 - X32 = 4 (correct) X34 - X33 = 4 (correct) If we now assume that only the last term on the LHS is to be multiplied by 0.92, we get for the first 10 expressions: X14 + X24 + X34 + 27.6 = 127.2 (not 130) X14 + X24 + X34 - 9.2 = 90.4 (not 90) X14 + X23 + X33 + 9.2 = 100 (correct) X14 + X23 + X33 - 18.4 = 72.4 (not 70) X13 + X23 + X32 + 13.8 = 95 (correct) X13 + X23 + X32 - 9.2 = 72 (not 70) X12 + X22 + X31 + 9.2 = 78.4 (not 80) X12 + X22 + X31 - 9.2 = 60 (correct) X12 + X21 + X32 + 4.6 = 65 (correct) X12 + X21 + X32 - 9.2 = 60.4 (not 60) So, some of the equations are spot on, some are close but others are 'miles' out! Clearly, it would be impossible to write a program to produce the answers in the book because they're just not wholly consistent with the given equations.

Nico Darmawan · Answer

To : Vulpes Sorry to make you confuse, i just repair the sentences / statements above. Please take a look again. :) My lecture just told to me to make the application based on the books, so when i asked him, he told me to look at the book again. The book just give the answer : lambda = 0.92 --> it means the result of the syntax above is 92% perfect. x11 = 52.4 x12 = 56.4 x13 = 60.4 x14 = 66 x21 = 0 x22 = 12.8 x23 = 16.8 x24 = 21.6 x31 = 0 x32 = 4 x33 = 8 x34 = 12 The book is not telling the way how to find these result. Just said : use reguler linear programming! So when i change the expression / syntax, i cant found the answer because i dont know the way to find it... Example : X14 + X24 + X34 + 30 lambda = 130 --> if i change the 130 to 160, i dont know how to find it... As well as others... Its make me crazy. Whats your opinion / suggestion sir? Thank you very much for reply my thread. I appreciate it. :)

Vulpes · Answer

Well, I assume 'lambda' is referring to lambda expressions but, for the life of me, I don't see how they can help with solving a system of linear simultaneous equations which is a mathematical problem, I think you're going to have to ask your lecturer for clarification on what the following is supposed to mean: X14 + X24 + X34 + 30 --> lambda = 130

Nico Darmawan · Answer

To : Vulpes Sorry you miss the problem... X14 + X24 + X34 + 30 ? = 130 --> ? is 'lambda" I have read a book with this problem. And my lecture told me to make an application like that. All the answers are all in the books except one, that is there is no explanation the way how to get the value. The book just say : "The form above can be solve with linear programming" --> Its make confuse. Can you help me. Thank you.

Nico Darmawan · Answer

To : Jaganathan Bantheswaran There is no input sir. Maybe i think the input are the expression / syntax it self like : X14 + X24 + X34 + 30 lambda = 130 X14 + X24 + X34 - 10 lambda = 90 X14 + X23 + X33 + 10 lambda = 100 X14 + X23 + X33 - 20 lambda = 70 X13 + X23 + X32 + 15 lambda = 95 X13 + X23 + X32 - 10 lambda = 70 X12 + X22 + X31 + 10 lambda = 80 X12 + X22 + X31 - 10 lambda = 60 X12 + X21 + X32 + 5 lambda = 65 X12 + X21 + X32 - 10 lambda = 60 X11 + X21 + X31 = 60 X14 + X24 + X34 = 150 X12 - X11 = 4 X13 - X12 = 4 X14 - X13 = 4 X22 - X21 = 4 X23 - X22 = 4 X24 - X23 = 4 X32 - X31 = 4 X33 - X32 = 4 X34 - X33 = 4 Xij = 0 (i = 1,2, ... , m ; j = 1,2, ... , n) And just want to get the value (output) for lambda, x11, x12, x13, x14, x21, etc. Thats all. My mathematic is bad, so i try to make an application to get that output / value. Can you help me? Thank you.

Vulpes · Answer

It's not possible to solve that particular set of linear simultaneous equations because they are inconsistent! If you simplify the equations by moving the constant terms to the RHS and then remove the 2nd, 4th, 6th and 8th equations which are duplicated, you're left with these: X14 + X24 + X34 = 100 => (A) X14 + X23 + X33 = 90 X13 + X23 + X32 = 80 X12 + X22 + X31 = 70 X12 + X21 + X32 = 60 => (E) X12 + X21 + X32 = 70 => (F) Inconsistent with (E) X11 + X21 + X31 = 60 X14 + X24 + X34 = 150 => (H) Inconsistent with (A) X12 - X11 = 4 X13 - X12 = 4 X14 - X13 = 4 X22 - X21 = 4 X23 - X22 = 4 X24 - X23 = 4 X32 - X31 = 4 X33 - X32 = 4 X34 - X33 = 4 It can now be seen that (A) is inconsistent with (H) and (E) is inconsistent with (F) because the same three variables can't add up to different totals. Incidentally, you'll be hard pressed to write a program which can solve a set of linear simultaneous equations yourself, even if you only have one set to solve. It's better to use a library. Here are a couple of free ones: http://www.codeproject.com/KB/recipes/matrixoperations.aspx http://www.lutzroeder.com/dotnet / (use Mapack)

Jaganathan Bantheswaran · Answer

Hi, What is input here, what should be output? What is the error? Explain more.

Linear Programming In C#

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