Sometimes teachers field stories like this to foster critical thought and encourage insightful book reports. It's stimulating material even with a flawed premise, and that's the point.

My teachers always seemed to be the type that had these stories in the curriculum, but weren't the type to follow up with the thinky-thinky bits. This had rather predictable results.

The ship was built as simply as possible and fueled with the precise amount needed for it's weight, there was nothing else to jettison besides the young woman. The plot was intentionally structured around an impossible scenario because the editor of the magazine the story originally appeared in wanted to subvert the "engineer action hero saves the day with a clever idea" trope that was common when it was written. The heavily contrived scenario is the weak point by most people's estimation, but overall the writing is well done and characterizations are very good.

The story bugs a lot of people due to the total lack of any safety margin for such an important mission as delivering emergency medical supplies. A guy named Don Sakers even wrote a rebuttal called The Cold Solution that was meant to point out a few things the original story overlooked without the idea of a bare minimum ship being changed.

Nah, in the future we'll have Space Force and no OSHA