Let us assume length of the room be x and width of the room be y.
Let further assume that room is rectangular.
Define area as a function of x and y i.e.
`A(x,y)=x xx y`
If relation between x and y is known to us then A(x,y) can be transformed into a single variable function either in x or in y.
Now let hythetically assume that average area B(x,y) requred an individual is known in term of lenth and width relation with that dimension of the room.
Define Lagranges function
`(delL)/(delx)=0,(delL)/(dely)=0, and (delL)/(del lambda)=0`
Solve for x,y and lambda .Calculate second derivative and apply test when it give max or min.
By this method you can estimate min /max .
do you have another method? by just using derivatives.