The landlocked University of Arizona, aided by the Coca-Cola Co., has found out how to turn impotent shrimp with finicky appetites into what could be a multi-million-dollar Mexican business.

After five years of research -- much of it supported by Coca-Cola -- the governors of Arizona and Sonora, Mex., last month announced plans to build a $500,000 commercial shrimp farm at Puerto Pennasco, Sonora, a shrimping fleet town on the Gulf of Mexico about 210 miles south of here.

The one-acre farm, which will take six months to build, is expected to produce between 40,000 and 60,000 pounds of tails -- beheaded shrimp -- a year, with a wholesale value of up to $250,000, Carl N. Hodges, director of the University of Arizona's Environmental Research Laboratory (ERL), says.If it does well, it may be used as a prototype for a much larger Sonora shrimp farm, he says.

The small farm will represent the conquest of several sticky problems that have plagued shrimp researchers for years -- not the least of which were the shrimps' stubborn refusal to mate outside their natural ocean environment or thrive on what man gave them to eat. The problem-solvers were scientists from Hodges' Tucson-based lab and the University of Sonora.

ERL and Sonora researchers originally went to Puerto Pennasco to work on experiments using desalted sea water for vegetable farms housed in large, air-inflated plastic buildings called "aquacells." In the early 1970s, they switched from vegetable to shrimp farming, which Hodges describes as "a form of agriculture for the desert sea coast that bypasses the need for fresh water."

Shrimp farms that actually were more like shrimp corrals have been built before. The nearest successful one in the United States is Mari Farms, Inc., a private venture in Florida, Hodges says. At the time ERL's experiments began, Mari had spent more than $4 million in three years for one 500,000-pound harvest, half the production expected.

The shrimps' problems were many. They wouldn't mate in captivity, so farmers had to catch female shrimp in the wild, looking for those with "viable" eggs, Hodges says. Maybe 10 shrimp in every 1,000 would release eggs in captivity, a low ratio that Hodges says is offset by the 150,000 to 200,000 eggs each female releases.

"But other experiments were at the mercy of nature because there was no opportunity for selective breeding," he says.

In 1973, ERL shrimp successfully reproduced in captivity, as did some of their offspring. The scientists now are working on breeds that grow larger and more rapidly than their wild cousins, although they still rely on wild shrimp for most of their experiments. Some of ERL's "mother and father shrimp," as Hodges calls them, are more than a foot long, and two or three would make a substantial meal.

More time, however, was spent developing a shrimp food than working on reproduction problems, Hodges says. Shrimp, which he describes as "sort of leisurely eaters," required a low-cost food that didn't dissolve in water, smelled good as far as they were concerned and contained all the right vitamins. Literally hundreds of other ingredients had to be added to a wheat-based food before it satisfied the shrimp.

"I've become a great believer in vitamins since working with shrimp," Hodges says. "They go downhill fast if they don't get all the right ones."

Counting the semitransparent shrimp posed another problem because the existing Sonora lab, which hatches a million shrimp a month, needs to keep a weekly count to detect any coming crises. The scientists believe that the best way to keep up with them is to count their eyes and divide by two.

That's not quite as difficult a chore as it sounds, because the shrimps' eyes reflect light that shows up as tiny dots in photographs taken with a flash camera. The dots could be counted rapidly with the right optical equipment, Hodges says, although his lab hasn't had the funds to do so and must rely on periodic sample counts of about 6,000 shrimp.

In all, the shrimp experiments have cost about $3 million, a third of that paid by Coca-Cola during the last two years after the experiment's major underwriter, Resorts International, optioned its rights to Coke.

"You might ask a university professor why he's working with a company that bottles a brown liquid that makes cavities in kids' teeth if they don't brush regularly," Hodges prompts.

"Well, I think it's an example of the positive side of multinational companies. Coke's philosophy is that, to operate internationally in the modern world, you have to be able to do things to benefit people of the countries you're in."

Coca-Cola also will benefit financially in any large-scale shrimp farm that's built. Although the exact ownership of both the prototype and any other larger farms still is tangled in Mexican legalities, Hodges says a majority interest will be Mexican-owned, with Coca-Cola to have a minority ownership role and the rights to use the technology on a world-wide basis.