Garfinckel, Brooks Brothers, Miller & Rhoads Inc. yesterday reported an increase in profits from $13.3 million ($2.92 a share) in 1978 to $15.2 million ($3.40) for its 1979 fiscal year ended Feb. 2.

The retail firm also reported income from continuting operations of $14.5 million, just below $14.7 million in fiscal 1978. Garfinckel's sold the Joseph R. Harris retail operation during the year.

Garfinckel's also reported sales for the year of $420.3 million; fourth-quarter sales were $139.4 million, up 5.5 percent over the comparable quarter last year. The company noted that the prior year's quarter was one week longer.

Garfinckel's profits for the fourth quarter were $8.4 million ($1.90), up from $7.7 million ($1.69) for the same quarter last year.

In a related development, a Garfinckel's official, Robert Vandemark, told a group of securities analysts in New York yesterday that the company expects to increase its capital expenditures to $31 million in 1980 from $17.5 million last year.

Vandemark also told the analysts that the company plans to add 25 stores this year to the 230 stores it was operating at the end of last year.

American Management Systems Inc., an Arlington computer and consulting firm, yesterday reported a 20 percent increase in profits from $1.4 million in 1978 to $1.7 million last year.

But as a result of the company's first public stock offering, per-share profits dropped from $1.28 to $1.21, the company said.

The firm's revenues increased 51 percent to $48 million from $31 million in 1978.

American Management reported fourth-quarter sales of $12.9 million, up 42 percent over the same period last year, and profits of $453,000 (31 cents), down from $567,000 (50 cents) for the same period in 1978.