Prince George's County last week officially opened a day care center in Upper Marlboro for the children of county employes, the first of its kind in the state. County Executive Parris Glendening said he hoped it would become a model for businesses and other Maryland counties, some of which have already sent representatives to take a look.

A county task force on child care issues last year had emphasized the "growing need for convenient and affordable child care," Glendening said. "Since we have asked the business community to provide child care , we felt that we should be a model." With an initial investment by the county of about $15,000, the center opened on a small scale several months ago in county-renovated church facilities, but with just a few children. The county held its grand opening ceremony last week as it geared up for full operation.

County Council employe Pat Warman, who enrolled her 2-year-old son, Stephen, in the center a month ago, said it has changed their lives.

No longer does she have to drive more than 10 miles out of her way to leave Stephen with a baby sitter, the Upper Marlboro resident said.

Instead, she drops Stephen off less than half a mile from the county administration building, where she works as an administrative assistant to the clerk of the County Council. She is sometimes able to visit her son at lunch, she said.

As for Stephen, "He seems to love it," said Warman. "He gets a lot more physical activity, he gets to play with more children and he puts in a harder day now than he did with the baby sitter. He has a very structured day."

In the Washington area, only the District operates a similar service, a day care center for children of employes in the Department of Human Services.

The Prince George's center is open to all county employes, including those of the county government, the school system and the Prince George's divisions of the Maryland-National Capital Park and Planning Commission, said Phyllis Diggs, the county's assistant chief administrative officer for human services. About 1,500 county employes work in the Upper Marlboro area, she said.

Located in the First Baptist Church next to the school system's Sasscer administration building, the center operates from 7 a.m. to 6 p.m. Monday through Friday. Children ages 2 to 5 are eligible to attend and, as of last week, 24 children were enrolled, said director Lynn Baldwin.

That number will nearly double in the next few weeks, she said, when equipment for two new classrooms arrives. The seven-classroom facility has a capacity for 60 children and should be full by September, Baldwin said. The county plans to expand the center to include infant care by 1987, she said.

The fee is $50 a week, Baldwin said, noting that private day care facilities charge as much as $100. The center must have 31 children enrolled to cover about $80,000 in costs annually, officials indicated.

A recent report by the Metropolitan Washington Council of Governments identifies Prince George's as having the the highest need for day care in the Washington area, Glendening said last week. Two-thirds of mothers in the county with children under 6 work outside the home.

"And that's only the tip of the iceberg," he said. "We now have more single-parent households than ever before, and more families with both parents working."

There are about 45,000 children in Prince George's under the age of 6, Diggs said, and about 18,000 slots available in licensed day care facilities in the county. Most of the remaining children are taken care of independently, she said.

But she added that the parents of an estimated 5,000 children under the age of 6 have "great difficulty" finding adequate day care.

The county's new "extended day" work-place schools, which are open from 7 a.m. to 6 p.m. and provide elementary students with academic services and day care before and after school, have helped alleviate the day care shortage, Glendening said, and will be expanded next year.

School spokesman Brian J. Porter said about 550 elementary students are enrolled in the extended day schools. Of those enrolled, nearly 150 are first grader, he said. The fee is $27.50 per week and will increase to $30 per week in September.

The need to provide convenient and affordable day care is a reality that businesses, including governments, are going to find increasingly difficult to ignore, said Ruth Crone of the Metropolitan Washington Council of Governments.

"As an employer, it's vital to them to have a work force that is available and ready to go -- not one that's worried about what is happening at home with the kids," she said.