Question

can someone explain what a free variable and a basic variable are? And how to find them

Answer 1

It might be better if you presented a particular linear programming problem. The definitions may be laborious and unhelpful.

Answer 2

ok...umm

-x+2y+3z+4a=5
y+a=-1
a=2

Answer 3

@tkhunny

Answer 4

There are no constraints on x or z?

Answer 5

no.

Answer 6

its an example in my notes...except its x1 x 2 x3 x4
i changed them so it doesnt get confusing

Answer 7

so what is a free and basic variable

Answer 8

Isn't a "Free Variable" simply every variable used in the original Objective Function, prior to the application of any Slack Variable?

Answer 9

my prof wrote it as a variable that can be assigned any value independent of the values and the system will remain consistent

Answer 10

Thus my hesitation. Definitions are not necessarily standard. Or, more accurately, one may SAY it differently and it will be difficult to know that we're talking about the same thing.

It seems to be leaning this way:

Basic Variable - Any variable currently exerting a constraint on the system.
Free Variable - Any other variable. I presume there are constraints in the FREEness of the free variables.

Answer 11

I expect x and z are free variables in your definition. It is not that you can assign z any value you wish, per se, but if you assign z a value, you can then assign z value to x that will preserve the original condition of the system.

Answer 12

Seriously, I just read up on this stuff. It appears I need to go read up on it again!

Answer 13

he said x,y and z r basic ...but the set x,y a are not

Answer 14

to me, FREE variables are the variables we can arbitrarily apply values
BASIC variables are the variables we cannot set their values
in your example, the system gives you a =2, you cannot change its values --> a is basic
a =2 --> y = -3 , this variable is basic, too. because we cannot change it
among x, and z , we choose either of them to be FREE, let choose z
so x = 2y + 3z +4a -5
z is independent variable, we can arbitrary let z = ..... whatever we want
whenever we change z, x changes, too. JUST depend on z only.
so, x is dependent variable.
DAT WAT I THOUGHT