The article on Elizabeth Dole's resignation as Secretary of Labor {news story, Oct. 24} quotes an ''administration source'' as saying, ''In a Republican administration, the business community is the core constituency (of the Department of Labor).'' The comments of the unidentified ''union leaders'' and AFL-CIO President Lane Kirkland suggest that they believe it is the job of the secretary of labor to do whatever the unions want.

Shouldn't the secretary of labor be dedicated to looking out for the interests of working people, in keeping with the law and sound economic policy, regardless of the mean, narrow, shortsighted or institutional demands of unions or business?

Unfortunately, the job is usually treated as a political throw-away where the Democrats reward and the Republicans (without success) try to placate organized labor.

With the economic problems we are facing, the Department of Labor is no place for trying to win popularity contests with noisy interest groups. Wage earners, union and nonunion, appreciate this proposition far more than the political technicians give them credit for. It is already past time to take labor policy and this job seriously.

DONALD L. DOTSON Arlington

The writer was an assistant secretary of labor from 1981-1983 and chairman of the National Labor Relations Board from 1983-1987.