Aqueous two$-$phase extraction is used to purify a recombinant HIV$-3-$galactosidase fusion peptide produced in Escherichia coli. For optimum separation, $450$ kg of a mixture of $19\mathrm{.}7\%$ w$/$w polyethylene glycol $($PEG$)$ and $17\mathrm{.}7\%$ w$/$w potassium phosphate salt in water is needed. Left over from previous pilot$-$plant trials is $100$ kg of a mixture of $20\%$ w$/$w PEG in water, and $150$ kg of a mixture of $20\%$ w$/$w PEG and $25\%$ w$/$w salt in water. Also on hand is $200$ kg of an aqueous stock solution of $50\%$ w$/$w PEG, $200$ kg of an aqueous stock solution of $40\%$ w$/$w salt, and an unlimited supply of extra water.

If all of both leftover mixtures must be used, how much of each stock solution and additional water is required?