HELP!!Extremely difficult calculus problem!!! Optimising to find the maximum volume.
where is the question? i dont see it
that method is really complex, i mean is there any other way rather than using 3d graphs???If you assume the cuboid's lateral dimensions to be (x,y), the point of contact at (x,y,z) with the ellipsoid will give you its height. Then given the various constraints you have - find (x,y) that maximizes the volume... There will be several points at the ends of these intervals that could be the maximum, but you have to look for local internal maxima as well.
Cool, so that would just be x+y+z= 18, i cant download autograph (the only best 3d graphing software). I am super curious about how the graph of this might look like. Any ideas about the software?If you let the axis of the ellipse be (a,b,c) and the cuboid have the size (2x,2y,z) - the point of contact is defined by
Maximize x*y*z with this constraint.
(x,y)=(0,36) would have zero volume so, no, that is not a maximum, local or otherwise.