There really isn’t anything in the breed description from this website (that I find to be fairly accurate) that indicates they wouldn’t be a good farm dog other than the usual lots of exercise and experienced hand.
http://www.dogbreedinfo.com/rhodesianridgeback.htm
The Rhodesian Ridgeback originated in Zimbabwe and worked as a hunting dog and as a retriever, took care of children, and guarded property. It descended from crosses between ridgebacked dogs who were imported by Boer settlers in the 16th and 17th centuries that were originally kept by native tribes in South Africa along with breeds such as the Khoikhoi dog, Mastiff, Deerhound and possibly the Great Dane. Its standard, fixed in Rhodesia, dates from 1922. Reverend Helm introduced two Ridgebacks into Rhodesia in 1877. Big game hunters soon discovered, that if used in packs they were excellent in hunting lions on horseback, hence the breed’s other name, the “African Lion Hound”. The dogs did well in the African heat of the day and the damp, cold nights. The breed was imported to the United States in 1950. The Rhodesian Ridgeback was recognized by the AKC in 1955.
A fine hunter, the Rhodesian Ridgeback is ferocious in the hunt, but in the home it is a calm, gentle, obedient, good dog. Good-natured, but some do not do well with small children because they may play too roughly and knock them down. They are intelligent, skillful and straight-forward dogs that are loyal to the family. They are brave and vigilant. Can be reserved toward strangers, socialize well. They possess considerable stamina and without enough mental and physical exercise they can become high strung and unmanageable. This breed needs a firm, confident, consistent pack leader who can provide rules the dog must follow and limits to what it can and cannot do. Meek and/or passive owners, or owners who treat the dog like a human rather than a canine will have a hard time controlling this breed and may also cause them to become combative with other dogs. When given what they need as the canine animal they will be excellent companion dogs, but are not recommended for most people, as most do not have the time nor energy to put into them. Ridgeback’s react best to an extremely consistent and firm but calm approach to training. They are intelligent and learn quickly, but will be stubborn and willful if they are stronger-minded than the humans. Training should be gentle, but firm and should start young while the dog is still small enough to manage. They are also very good watch dogs, but not suggested for guard dogs. They are very protective of owners. This has to be addressed during their early training. This breed can be more destructive than a Lab if not given enough exercise and is not convinced the humans are his authority figure. Do not overfeed this breed. Provided this dog meets cats and other pets when it is young, any potential problem will be prevented. Ridgebacks make excellent jogging companions.
http://kodaridgebacks.com/breed_info/temperament
http://www.rrcus.org/club/breedinfo/RRFAQ.htm
these folks raise RR, goats and alpacas…http://fragglerockfarm.net/rhodesian.htm
these guys too…http://www.laidbacklionhounds.net/products.html
In fact, searching for Rhodesian Ridgeback and farm brings up a whole lot of them living happily on farms with kids…
This RR obviously didn’t know that she’s a viscious sight hound killer-she nursed and raised a rejected runt piglet as her own. http://www.dailymail.co.uk/news/article-1210909/Abandoned-piglet-lost-hound-Giant-farm-dog-saves-baby-pigs-bacon-adopting-own.html