In my textbook, it says that monopolistic competition will never lead to productive efficiency (where $MC=AC$) in the short run and long run. I understand that they are meant to be producing at the profit-maximising level of output (where $MC=MR$), but all the diagrams showcase scenarios where the $AC$ curve is always positioned such that the points where MR=MC does not intersect where $MC=AC$.
My question is, is there any possibility that the profit-maximising level of output will also happen to be where we've achieved the lowest possible unit cost (lowest $AC$)? So that $MC=MR=AC$, and the firm can be both productively-efficient whilst also being profit-maximising? Why is this not possible?