ILL 1987 Problem 18

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.

Dataset text AoPS wiki problems. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.