The Department shall make a careful physical and mental examination of every child committed to it by the courts, investigate the personal and family history of the child and his environment, and place such children at such facilities as are available. Any children committed to the Department and afterwards found to be eligible for commitment by proper proceedings to any state hospital or admission to a training center for individuals with intellectual disability shall take precedence as to admission over all others and shall in all cases be received into the state hospital or training center within 45 days.