Question

How do you get the maximum function out of a linear programming simplex table? I have the table and it is correct according to the mark scheme but how on earth do you get the function out of there?

Answer 1

This is the table

Answer 2

Oh and all the fractions are in thirds, sorry for the hand writting

Answer 3

How much can P increase before (4) exceeds 20?

Answer 4

0 times?

Answer 5

?? If that's a correct answer, then I totally cannot read your tableau. You'll have to do a better job of communicating the information. Sorry.

Answer 6

I don't really get what you are asking :(

Answer 7

Your task is to transition from a feasible solution to an optimal solution. You need a process for that. Are you saying you went to all that trouble to learn how to construct the tableau, but managed no idea how to use it? I am quite puzzled by this.

Find a variable that will increase the Objective Function. Find how much you can increase that variable.

What is the "most negative" value right now in your objective function? That's where we start.

Answer 8

Then the smallest positive ratio to pick the first pivot point. It looks like you did that. Now what?

Answer 9

Okay, I see my confusion. Please do two things...

1) What is that "P"? It seems to serve no purpose.
2) Find a different way two write the variable "x". Very, very confusing. About half the time, I think your "x" is actually "2r" and that just didn't make any sense. Don't apologize for your handwriting - fix it so that it's clear.

Your solution is fine. You have it as (x = 0,y = 5). This is the solution. In this case, you can confirm graphically.

Answer 10

P.S. Sorry for jumping on you. I was just super not understanding what you were doing until I made those two realizations.

Answer 11

Thank you so much that helps quite a lot. I am learning from a text book which is how I learnt to make a tableau but after it was constructed in the instructions it just stated the soloutions from them.

But where specifically in the tableau do you read the (x = 0, y = 5) from? I can see the y = 5 yet not the x.

Answer 12

Nor does the book describe what the P does it just kinda sits there redundant

Answer 13

It's "=0" until you say otherwise.

When you selected the y-column as your pivot column, you can expect the next feasible solution to contain "y = ".

After one round of reductions, your current feasible solution is (y = 5, t = 7 for a total of 20) You can read this from the reduced columns in the tableau and compare them to the right-hand column.

Answer 14

That is perfect, thank you so much for your time and helping :D!