Let
be a parallelepiped with
. Prove the inequality
In what cases does equality hold?
Proposed by France.
%V0
Let $ABCDEFGH$ be a parallelepiped with $AE \parallel BF \parallel CG \parallel DH$. Prove the inequality
$$AF + AH + AC \leq AB + AD + AE + AG.$$
In what cases does equality hold?
Proposed by France.
Školjka