They will charge for delivery
You should call them up and give him the exact size you need. I would go with 5/8 or 3/4 plywood. They may charge you to deliver.
If you plan to use it to support a mattress, it will not be very strong. You would need to add slats under the plywood. If you are using a box spring, you can skip the plywood and just use the slats. I would recommend 5 pieces of 5/4 deck boards cut to length.
You may have to rent their truck for delivery but they do cut plywood sheets to your specifications
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