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How to use optimization in matlab?

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Greetings everyone, I am new to Global Optimization Toolbox.
Could someone explain to me please, I have the following simple code, which represents a square with side A and B.
Basically I am just trying to find value of x which would maximize my V (Volume).
How would I do that with an optimization toolbox? Any help would be much appreciated.
(I have Global Optimization Toolbox and Optimization Toolbox)
x = 0.2 %Optimization Variable <---
Lt = 10; %Total Perimeter Length
A = Lt*x % Side A
B = Lt-A % Side B
V = A*B %Volume (We want to maximize Volume)
rL = A+B

Accepted Answer

Alamanda Ponappa Poovaya
Alamanda Ponappa Poovaya on 24 Nov 2021
It appears you want to find the maximum area of a rectangle with sides A and B, such that A + B = Lt. This would assume that Lt is the semi perimeter of the shape. Regardless, this will not effect the Optimization variable x, but you may want to modify the code below, as if Lt is the perimeter, A = (Lt*x)/2 and B = Lt/2 - A
% range of x - from 0 to 1, as sides can have
x1 = 0;
x2 = 1;
%Semi perimeter = 10
Lt = 10;
%x is optimization variable
[x_max , val] = fminbnd(@(x) -(Lt*x)*(Lt-Lt*x),x1,x2);
%val is minimum
val = -val;

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