Hi guys. I was solving 3 problems of this kind, two went pretty good, I will just ask if they are correct and the 3rd one... Yeah , I couldn't manage to finish it ,so I would need a petite help Well I'm not very good in using latex so it looks how it looks, I hope you won't have a problem to read the algorythms So here it is:

Problem nr 1 (solved, tell me if it's correct ):

With use of simplex algorythm,maximalize the following function: with: oraz :

And this is what I've done myself

I don't know if you use the same name , but now I have to chose Pivot element(?).I took the .After I've done the following actions: II. line - I. line, III. line + I. line,IV. line - I.line , V.line + 2*I.line. Results:

Now my Pivot element is: . My following actions: I + IV , II - 2*IV, III without changes, V +2*IV, Results :

Pivot element: . Following actions : I + III, II without changes, IV + III, V +III. Results :

Answer:

Btw: I was using so called 3 Phase method , I hope it tells you anything...

Problem nr 2 (also just tell me if it's correct or not )

With use of simplex algorythm,maximalize the following function : with and:

Now I needed to create the algorythm.I need to maximalize the function so I multiplied the funtion with -1.I also needed to change the signs in 1st and 3rd inequality so I also multiplied them with -1. It was written in instructions for 3 Phase method ,so I did so And my algorythm looks like this:

Pivot element : . In the description of the problem,it was written,in phase 0 to chose an element that will not follow to decimal numbers. Following actions: I - V , II + 2* V , III - V , IV + V, VI + V. Results:

Pivot element: .Following equations: I - IV , II - IV , III without changes , V + 2*IV , VI + 2*IV. Results:

Pivot element: . Following equations: I - II, III - II, IV without changes, V without changes, VI + 4*II , Results :

In line all elements are , so I can already finish the algorythm and have following results:

Answer:

Problem nr 3 ( this is where I need your helps solving this )

With use of simplex algorythm, minimalize following function : and :

Of course first I've changed the sign in the first inequation and after created following algorythm:

Pivot element : (of course it was written to chose an element in phase 0, that will not result in decimal numbers) .Equations : I + IV, II - 2*IV, III without changes , V - 2*IV. Results:

Pivot element : .Equations : I - 2*II, III-II, IV-2*II, V-II, Results:

Pivot element : . First, i divided this line through 2 so the pivot element could be = 1. And after following equations : II+I, III without changes, IV- 2*II, V-2*II ,Results:

Till here it's fine but from now one everything starts to be complicated and senseless. Theoretically now I need to chose a column where is higher than 0. So I have this "1". So ok, I chose the last line ,which wasn't changed yet ,but after equations I still have one element of ,which is positive,and it shouldn't be so... So I don't know where I went wrong... Anyone has some ideas? Thanks