Minnie is Carrie's older sister, with whom Carrie stays when she first gets to Chicago. A new mom, Minnie and her husband, Sven, live a simple life devoid of luxuries. Marriage to Sven, it seems, has shaped Minnie's valuing of industry and responsibility:
[Minnie] had changed considerably since Carrie had seen her. She was now a thin, though rugged, woman of twenty-seven, with ideas of life coloured by her husband's, and fast hardening into narrower conceptions of pleasure and duty than had ever been hers in a thoroughly circumscribed youth… (2.25)
In Carrie's view, Minnie's commitment to hard work doesn't cast her in the most flattering light: "Her sister carried with her most of the grimness of shift and toil" (1.62).
Minnie's austere lifestyle makes her serious foil material for Carrie.