On Jan. 17, Safeway stores in Washington were offering choice boneless sirloin tip roast for $1.39 a pound.

The same day, slaughterhouses in Colorado were paying farmers 37 3/4 cents a pound for 1,1000-pound, corn-fed steers from which such steaks are cut.

The $1.01 1/4 difference is the subject of heated arguments among farmers, packers, meat wholesalers, retail chain stores and consumers.

Is such a markup justified? Consumers and farmers usually say it isn't; the beef middlemen say it is.

Here is what happened to the farmer's steer.

The packer paid $415.25 (37 3/5 cents a pound) for the live, 1,1000-pound animal.

But the caracass of the slaughtered animal weighed only 680 pounds, so the cost of the meat and bone to the apcker actually was 61 cents a pound.

Not all of that carcass could be served up as chucks, ribs, loins, sirloins and rounds, though. (There is only about 13 pounds of tendeloin on a full-grown steer.) Much of the carcass is fat and bone that has to be trimmed away. And the carcass also loses about 13 pounds as it dries in the packer's cooling room.

Restaurant and retail cuts on such a carcass probably weigh only about 480 pounds. These cuts sold to chain stores in mid-January for about $450 or an average of slightly less than 96 cents a pound. The seller could have been a packing company, if it had a facility for meat cutting or it dealer who buys carcasses and breaks them down into the primary cuts.

About 75 pounds of fat still had to be trimmed off those 480 pounds of cuts before they could be put in the display counter. That brought the weight of the meat down 405 pounds. So the retail store that paid $450 for all those cuts actually was paying almost, $1.10 a pound for them not 96 cnets.

And in January, the average of all the cuts sold at that kind was about $1.37 a pound. The retail stores say the 27-cent difference goes to pay butchers and checkers, and for packaging and overhead - and a small profit.

Between packer and consumer also were transportation costs (4 1/2 cents a pound from Colorado to the East Coast) and storage costs.

But there also were opportunities for profits. The carcass probably produced about 75 pounds of hamburger meat in addition to the cuts. And the packinghouse more than offset the cost of killing the animal by selling its hide, organs and inedible parts.