# How to find the optimal solution between boundary values?

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ancy s george on 1 Jun 2022
Answered: M Mirrashid on 5 Jun 2022
If a problem a*x+b/x+c
subjected to 0<x<=d
Condition on a,b,c,d such that for optimal solution 0<x*<d?
For example,
x0=0;
f=@(x)(2*x+5/x+10);
x=fmincon(f,x0,[],[],[],[],0,10)
Local minimum found that satisfies the constraints. Optimization completed because the objective function is non-decreasing in feasible directions, to within the value of the optimality tolerance, and constraints are satisfied to within the value of the constraint tolerance.
x = 1.5811
If plotting this,
If I taking the range, 0 to 10 optimal point is 1.581,that is between the boundary
while in the range of 2 to 4,optimal point is 2,that is in the boundary
Also if the range 4 to 10,optimal point is 4,that is in the boundary
So,my problem is to find out at what condition on a,b,c,d such that solution between the boundary not on boundary.
N.B a,b,c,d values are changable.
##### 2 CommentsShowHide 1 older comment
ancy s george on 2 Jun 2022
ok sir,Thank you

Matt J on 1 Jun 2022
The derivative of the curve is zero at x=sqrt(b/a). So, the condition is,
0<a,
0<b,
sqrt(b/a)<d
ancy s george on 2 Jun 2022
Thank you

M Mirrashid on 5 Jun 2022

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