Hello, would appreciate any comment on the following. The side edges of a cut-out for an undermounted farmhouse/apron sink sit on the edges of the sink; the back edge is on the sink base cabinet, and there is no front piece. The side edges for a flushmounted sink sit ot the cabinets on both sides of the sink. What is the way to support one of the cut-out edges if a dishwashing machine is right next to a flushmounted sink instead of a cabinet? One corner of the cut-out is up in the air then. I guess a dishwasher is not to be used as a countertop support. Should a custom supporting structure be built? Thank you.

What kind of countertop material? You may need to make up an angle brace that would screw to the sink cabinet. Posting a picture may help.

Yes, sorry, it's confusing without a picture. Please see attached image: kitchen sink cabinet is retrofitted for farmhouse sink and the side panels of the sink cabinet are cut to make space for the same width sink. The right edge of the plywood (for countertop, either wood or granite) sits on a cabinet; the left edge is up in the air with no support (this is where a dishwasher is planned). Even plywood alone sags without support at this corner. What are good ways to build a support for c/top? Thanks.

Can't put a side panel like the one on the right? Cut the toe kick and it should look like a cabinet side.

Yes, full side panel of 3/4" plywood, toe kick cut out, and attached to left side of sink base.
Is there room to move the dishwasher over 3/4"?

Can't put a side panel like the one on the right? Cut the toe kick and it should look like a cabinet side.

Thank you. Yes, this will work.

Yes, full side panel of 3/4" plywood, toe kick cut out, and attached to left side of sink base.
Is there room to move the dishwasher over 3/4"?

Should be enough room. Thank you, plywood it is.