Final answer:
The correct response to the question is the Weimaraner, a breed named after the city of Weimar and not included in the provided options. It is known for its hunting capabilities and distinctive silver-grey coat.
Step-by-step explanation:
The sporting dog of Germany that was selectively bred by Grand Duke Karl August of Weimar, which is thus named after the city, is the Weimaraner. This breed is not one of the options provided in the question, but based on the information given and the historical significance, it is clear that the Weimaraner is the dog in question. The options provided (Dachshund, Doberman, Rottweiler, Schnauzer) are all German breeds, but they do not fit the description of being named after the Grand Duke Karl August of Weimar. The Weimaraner is known for its sleek, silver-grey coat and was originally bred for hunting. It became well-regarded for its abilities in the field as a pointer and retriever.