# Question:How to find the valid values of variables(combination) for given range of values of an expression?

## Question:How to find the valid values of variables(combination) for given range of values of an expression?

I am working on expressions with multiple variables ranging between 3 and 10. Each variable has a range for its value. Now I want to find out the possible combination of variable values satisfying expression value which is in certain interval.

I came across how one can find maximum and minimum value of the expression. But, My goal is to find all possible combinations of variables for the given range of expresison value.

`f:=2*a*b-3*a-2*b-c;`
`minimize(f, a = 0 .. 10, b = 1 .. 5, c = 0 .. 1, location);`=-13, {[{a = 10, b = 1, c = 1}, -13]}

`maximize(f, a = 0 .. 10, b = 1 .. 5, c = 0 .. 1, location);` = 60, {[{a = 10, b = 5, c = 0}, 60]}

But when I have a certain range for expression f [15..30].->f>=15 and f<=30

Is there a way to find out all combinations of variables with in this given range??

I have just started to study on Optimization and tried with QPSolve for optimal solution. I observed that QPSolve cannot take variable intervals, but takes inequalities as cnsts.

Optimization:-Interactive(f>=15,f<=30, a=amin..amax,b=bmin..bmax,c=cmin..cmax)

I am able to find the minimum and max possible combination but not all with in the range

EDIT: My final aim is to find out all possible combinations which do not satisfy the given condition. All combinations which fails the condition f>=15,f<=30

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