Question

*Please Someone Help!*
maximize P=1x+0.8y=0.7z
Subject to 30x+20y+50z(less than or equalto)<40
5x+15y+17z(less than or equal to)<8
x+y+z(greater than or equal to)>3.5

Answer 1

\[P=1x+0.8y+0.7z\]
Is The First One, I Messed Up On The First Post

Answer 2

This is a linear programming problem, and the best way to solve it is by using the simplex method. Do you know the method?

Answer 3

great linear algebra question

Answer 4

You could also draw it. P is a plane and the other 3 ones are 3-dimensional spaces, and you just need to find the intersection :)

Answer 5

Yes, That is when I have to add slack Variables. But that's as far as I can get

Answer 6

Good. You need to add only slack variables to the first two constrains since it's a maximization problem and they're less-than-or-equal constrains. But you need to add also an artificial variable to the last constrain.

Answer 7

If you're not familiar with the term "artificial variable", then it's a variable you add in order to get a feasible solution to the objective function.

Answer 8

30x + 20y + 50z + 1 + 0 + 0 + 0 = 40
5x + 15y + 17z +0 + 1 +0 + 0 =8
1x + 1y + 1z + 0 + 0 - 1 + 0 = 3.5
-1x - 0.8y - 0.7z + 0 + 0 + 0 + 1 = 0

Correct?

Answer 9

Almost!
\(30x + 20y + 50z + s_1 + 0s_2 + 0s_3 + 0a_1 = 40\)
\(5x + 15y + 17z +0s_1 + s_2 +0s_3 + 0a_1 =8\)
\(1x + 1y + 1z + 0 + 0 - 1s_3 + a_1 = 3.5\)

Answer 10

Where \(s_i\) represents the slack variables, and \(a_1\) is an artificial variable. The objective function will then be \(P=x+0.8y+0.7z-Ma_1\), where M is a very large positive number.

Answer 11

We never did the artificial numbers :-/

Answer 12

You can watch this lecture for better understanding http://www.youtube.com/watch?v=wdGiekwXM2w&feature=relmfu

Answer 13

Our professor completely skipped that

Answer 14

Did you study the dual simplex method?

Answer 15

You can use the dual simplex method to solve it if you know the method.

Answer 16

Yes, we did

Answer 17

You can use it, although I think it would be a bit lengthy.

Answer 18

You need to multiply the last constrain by \(-1\), and then add the slack variables.

Answer 19

Is the dual simplex method not only for minimization problems?

Answer 20

Not really! You can actually always convert a maximization problem to a minimization problem by multiplying the objective function by \(-1\). I still think using the artificial variable is better here. It would take you less than 30 minutes to learn it.

Answer 21

Let me ask you a question, are all the decision variables positive?

Answer 22

I think they are

Answer 23

@dmihail: I just saw your comment. Using graphical method with a three variables LP problem is difficult. It's probably the best method if you have two variables.

Answer 24

Im attempting to watch the video you posted. Sure wish i had this video before

Answer 25

Good luck. It won't be difficult to use artificial variables if you're already familiar with the method. :D

Answer 26

If you worked that problem out, would it even work? last time i had a problem like this it was a trick question that had no solution

Answer 27

What do you mean, would it even work?

Answer 28

correct. Would there be an answer for x, y and z?

Answer 29

I believe so!

Answer 30

Awesome Thanks. Will chat back if the video confuses me LoL

Answer 31

OK, if I'm still here :D

Answer 32

How would the problem look written out in a matrix form?

Answer 33

I'm not used to the matrix form, sorry!

Answer 34

Could you break it down using the simplex method. Im going crazy trying to figure it out. I have been working on it for almost a week and cannot figure it out

Answer 35

I'm busy right now. I'll write it down when I get time. When do you want the solution?

Answer 36

You can email me at any time today... vdooley777@yahoo.com I appreciate all your help

Answer 37

Ok.

Answer 38

Thank You So Much