1. The problem statement, all variables and given/known data A plane with equation xa+yb+zc=1 (a,b,c>0) together with the positive coordinate planes forms a tetrahedron of volume V=16abc (as shown in the Figure below) Find the plane that minimizes V if the plane is constrained to pass through a point P=(8,2,3) . Here is a picture: https://www.pic.ucla.edu/webwork2_course_files/12F-MATH32A-1/tmp/gif/dhattman-1243-setSix-prob8--image_14_8_31.png [Broken] 2. Relevant equations I used Lagrange multipliers SEVERAL TIMES. 3. The attempt at a solution I've gotten Partial(a)=(1/6)bc G(a)=-8/a^2 Partial(b)=(1/6)ac G(b)=-2/b^2 Partial(c)=(1/6)ab G(c)=-3/c^2 I then found that a=4b, 2c=3b, and 3a=8c but I am SO STUCK after this. Please help!