Cable television in Fairfax County is only "marginally feasible"because of the low population density in the sprawling 399-square-mile jurisdiction, according to findings of a consulting firm hired by the Fairfax Board of Supervisors.

The Washington-based consultants, Malarkey, Taylor Associates, released a study yesterday saying that investors in cable television will have to be able to endure losses for about 10 years before making a profit in the county, which has 192,776 households.

"A firm cannot come [into Fairfax] inadequately financed or it will more than likely go broke," Archer Taylor, a member of the consulting firm, told the supervisors yesterday.

Fairfax County, according to the study, is not an attractive area for cable television because of county requirements for underground cable construction in many areas and because a large number of television stations, can be received without cable.

Taylor said yesterday that, under the best financial conditions, a cable company could expect in 10 years to earn only 7 percent annual profit on a $30 million investment. He added that with high interest rates on borrowed money and the cost of installing underground cable, a long-term investment in a Fairfax cable system could be a "real disaster."

The Board of Supervisors commissioned the $35,000 cable television study last December and plans to award a cable franchise sometime next spring, after a new board is elected and sworn in.

Arlington County is the only major jurisdiction in the Washington area with a cable television system. In Arlington, where the housing per square mile - is more than twice that of Fairfax, regular cable service costs $7.95 cents a month and "Home Box Offices, which festures movies and special sports events, cost $16.90.

Alexandria has approved the idea of cable television and plans to award a franchise in June.

Taylor said yesterday that while bringing cable television to Fairfax is a risky financial investment, there are major cable firms interested in the area because of its prestige location near Washington and because of the county's long-range prospects for high profits.

Taylor said there are about 24 major cable companies in the United States able to afford a major investment in Fairfax. A company willing to suffer some losses for 10 years or longer, he added, could become very profitable in Fairfax, one of the nation's wealthiest counties.

The consulting firm advised the board that, in order to attract offers from cable firms, it should divide the county in half-allowing two companies to serve the jurisdiction reducing the amount of capital required to get one giant cable system off the ground.

The cable system should provide for local educational and informational programs and should turn over 3 percent of its gross annual profits tot he county, the consulting report said.

In other action, the supervisors granted a special exception to permit construction of a weight reducing and beauty resort on a 102-acre property near George Mason University.

The Fountains, as the resort will be named, will cost about $3 million, according to it developer, Dr. James J. Scheiner.

Guests, limited to 30 in number, will be tended by a staff of 25, including Scheiner, who is a medical doctor. Their regimen will discourage "pills, shots, fad foods [and] trick diest."

The board also voted to request a study by the county, in conjunction with local business and banking leaders, of ways to increase the number of available apartments in the county. Supervisor Marie B. Travesky (R-Springfield) said the county should look at ways to make apartments more profitable. Apartments have been shunned in recent years by builders in favor of more profitable townhouses and single-family houses.

Board of Supervisors also voted yesterday to chance county zoning laws to allow service stations to sell gasohol, the blend of 90 percent gasoline and 10 percent alcohol that has received extensive publicity in recent weeks with the sharp increase in the price of gasoline.