1. The problem statement, all variables and given/known data I've been struggling to figure out how to do the following problem which I came across: Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x+2y+3z=6. Show ALL of your workings. 2. Relevant equations N/A 3. The attempt at a solution Volume will=xyz, since each side is as long as the face in that plane. We need to maximize this. So we need to maximize xyz in the domain x+2y+3z=6 I tried getting x, y, and z by themselves with respect to each other and then subbing into the equation V=xyz. Then I would differentiate and set this equal to 0 to find the max. I don't think this is the correct way of doing it as it took huge amounts of time and became impossible to deal with owing to its complexity. At the moment in multivariable calculus we are learning minima/maxima, line integrals, double integrals, greens theorem etc.