@Jeanne - Simme Valley is right on the amount of feed. 1-2% of body weight. So a 4 mo jersey/bs cross should be weighing in the 250-300 lb range right now. So I would shoot for say 5 lbs right now.....a little over half a gallon bucket of feed. If he cleans it up then increase a little. A 5 gallon bucket holds APPROX 25 lbs of feed to give you an idea.
The jerseys will grow and start to flesh out at a younger age but a swiss takes much more time to grow bone before they will put on much meat/muscle. The fact that he is nursing is good as he will gain more milk fat/body. The biggest problem with most dairy cross animals is they will get a "hay belly" of pot belly if they don't get enough grain to keep their bones/body growing. It is typical in holstien calves that do not get the concentrates they need and eat mostly hay.
I raise jersey crosses for all my meat. I have several nurse cows that I put calves on to raise up and I will let them nurse for 5-10 months before weaning. Often doing as you do, and locking the calves away from the cow so I can milk for the house. I have raised a couple of swiss x holsteins. They just grow slower than the jersey crosses.
It is unlikely you will get enough meat on him to eat at 12 months. 18-24 months will be more likely. But if you can get him on good grain for the first 6-8 months and then add in more corn, you might be able to push it a bit. Just because of the nature of the swiss and the way they grow bone and body before they flesh out, it will take longer.
If you are milking your cow, are you breeding her AI?... is she the jersey or the swiss??? I would suggest if you want her calf to be beef for eating, to breed her to an angus of other beef breed. The calf will "fatten up" quicker. Most of mine I breed to a beef bull if I want to sell calves for raising for beef. If I am looking for a replacement heifer then I use whatever breed she is ( in my case jersey or guernsey) and I will use sexed semen so I have a better chance to get a heifer calf for a replacement