AT-OEMO-FED1 2011 Problem 4

Inside or on the faces of a tetrahedron with five edges of length $2$ and one edge of lenght $1$ , there is a point $P$ having distances $a, b, c, d$ to the four faces of the tetrahedron. Determine the locus of all points $P$ such that $a+b+c+d$ is minimal and the locus of all points $P$ such that $a+b+c+d$ is maximal.