Professor Halfbrain has spent his entire weekend by cutting lots of wooden $50\times50$ checkerboards into lots of polyominoes. He looked at various pattern polyominoes with area $49$, and always tried to cut as many copies of the pattern as possible out of some wooden $50\times50$ checkerboard. The pattern polyomino could be rotated and flipped over, but it always had to be aligned with the cells of the checkerboard. For most patterns, the professor was able to cut quite a number of copies while wasting only a small fraction of the checkerboard area.
Professor Halfbrain has also proved two extremely deep theorems on such checkerboard cuttings.
Professor Halfbrain's first theorem: For every possible polyomino pattern of area $49$, it is possible to cut at least one copy of the pattern out of a wooden $50\times50$ checkerboard.
Professor Halfbrain's second theorem: There exist polyomino patterns of area $49$, for which it is not possible to cut 52 copies of the pattern out of a wooden $50\times50$ checkerboard.
This puzzle asks you to improve the two theorems of professor Halfbrain and to make them even deeper. Find an integer $x$, so that "one copy" in the first theorem may be replaced by "$x$ copies", and so that "52 copies" in the second theorem may be replaced by "$x+1$ copies" (again yielding true statements, of course).