1. The problem statement, all variables and given/known data Find the dimensions of the box with the largest volume, given the constraint that the perimeter of the cross sector perpendicular to length is at msot 108 2. Relevant equations So I have f(x,y,z)=xyz and the constraint is 2x+2z<108 3. The attempt at a solution I set up the legrange multipler <yz, xz, xy>=(multiplier)<2, 0, 2> So then you have yz=2(multiplier) yx=2(multiplier) xz=0(multiplier) and then 2x+2z<108 But since xz=0(m), I can't figure out how to solve the 4 equations to get the possible points. If I have xz=0, then either x or z is 0, right? but then there would be no volume..any ideas? Thanks!