Mujikaku Tensai Renkinjutsushi no Henkyou Machizukuri: Boujakubujin na Ane no Kawari ni Hatarakasarete Ita Imouto, Henkyou Ryouchi ni Sasensareta to Omottara Matte Ita no wa Ouji-sama Deshita!?

Lumina, the younger sister, has been working diligently as an alchemist at the royal court in place of her older sister, who spends all her time playing around. She can't rely on her older sister, parents, or even her fiancé. As she endures her loneliness, her older sister and fiancé suddenly break off their engagement and inform her that she will be transferred to the frontier. Expecting to see them grieving over the loss of their position and fiancé, Lumina heads to the frontier, only to find that his majesty, Prince Elms of the Ratman Kingdom, is waiting for her! (Source: Kadokawa, translated)