1. The problem statement, all variables and given/known data Consider the tetrahedron in the FIRST octant defined by x+y+z/2=1. Find the maximum sphere inside the tetrahedron. 2. Relevant equations I use Lagrange Multipliers. let L be lamba. (del)f(x,y,z)=L*(del)g(x,y,z) 3. The attempt at a solution I don't know if I can assume that the center of the sphere is (a,a,2a) where 0<a<1 reason: Since the x, y, z intercepts of the tetrahedron are 1, 1, 2 respectively, I let the z coordinate of the sphere be twice the x and y coordinates. f(x,y,z)=(x-a)^2+(y-a)^2+(z-2a)^2 g(x,y,z)=x+y+z/2-1=0 next, take the gradient of f and g in the equation 2(x-a)i+2(y-a)j+2(z-2a)k=L*(i+j+k/2) solving for x, y, z gives x=L/2+a y=L/2+a z=L/4+2a put them into the tetrahedron equation and solve for lamba L L=8/9 * (1-3a) now put the value of L into the x, y, z equations which gives x=4/9*(1-3a)+a y=4/9*(1-3a)+a z=2/9*(1-3a)+2a thus, put those equations above into f(x,y,z)= 4/9*(1-3a)^2 therefore, the radius is r=2/3*(1-3a). Once we know the radius, we can maximize the sphere. Is my solution correct? If not, how do you do it?