MATLAB: How to maximise Volume of a cylinder such that its Surface Area is less than 10 using fmincon by predicting only either radius or height but not both

MATLAB

Volume= pi*r*r*h
Surface Area= 2*pi*r*(h+r);
i am solving a bigger problem. this simple example will help me to solve the bigger problem. The main point is Fmincon should predict only r or h but not both. The other value has to be computed through the constraint equation. Please give me the full code including function call, objective function and constraint function. Thanks

Best Answer

Not possible. Since r and h are interdependent, "fmincon" must be able to vary both and thus predict them simultaneously.
Of course, if we assume that maximum volume will result if we use maximum surface area, we have
10 = 2*pi*r^2 + 2*pi*r*h
and we can solve for h:
h = 5/(pi*r) - r
and insert in the volume formula
max: pi*r^2*(5/(pi*r) - r)
But for bigger problems with more constraints, this does not seem the way to go.
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