{x, y, u, v} /. #2 & @@
 List[Minimize[{x - 2 y^2, Q >= x >= y >= 0}, {x, y}],
   List[FindRoot[{v - Sin[u] == 0, v + u == 30}, {u, 0}, {v, 20}]]]~
  Flatten~1

{x, y, u, v} /. #3 & @@
 List[Minimize[{x - 2 y^2, Q >= x >= y >= 0}, {x, y}],
   List[FindRoot[{v - Sin[u] == 0, v + u == 30}, {u, 0}, {v, 20}]]]~
  Flatten~1