Super Mutants are sterile but humans are not. The Master intended to sterilize the last humans and let them die off, but this line of thought is fallacious and avoids a potential solution.
To put simply, the humans could be kept in a Vault so they could breed for creating more super mutants who are long lived though not immortal to my knowledge. A few generations of breeding humans would produce enough super mutants to keep up population growth. Only enough humans to continue repopulating without too many problems regarding potential incest are to be kept and prospective ascendants are taken away after developing into adults.
Eventually a final solution for sterility may be found and this measure won't be needed but could be kept up if the problem is perpetual.
To put simply, the humans could be kept in a Vault so they could breed for creating more super mutants who are long lived though not immortal to my knowledge. A few generations of breeding humans would produce enough super mutants to keep up population growth. Only enough humans to continue repopulating without too many problems regarding potential incest are to be kept and prospective ascendants are taken away after developing into adults.
Eventually a final solution for sterility may be found and this measure won't be needed but could be kept up if the problem is perpetual.