BG-MO 1988 Problem 3

Let $M$ be an arbitrary interior point of a tetrahedron $ABCD$ , and let $S_A,S_B,S_C,S_D$ be the areas of the faces $BCD,ACD,ABD,ABC$ , respectively. Prove that $$S_A\cdot MA+S_B\cdot MB+S_C\cdot MC+S_D\cdot MD\ge9V,$$ where $V$ is the volume of $ABCD$ . When does equality hold?