BG-MO 1973 Problem 6

In the tetrahedron $ABCD$ , $E$ and $F$ are the midpoints of $BC$ and $AD$ , $G$ is the midpoint of the segment $EF$ . Construct a plane through $G$ intersecting the segments $AB$ , $AC$ , $AD$ in the points $M,N,P$ respectively in such a way that the sum of the volumes of the tetrahedrons $BMNP$ , $CMNP$ and $DMNP$ to be minimal.

H. Lesov