how to create file in xml using c# Dynamically

<?xml version="1.0" encoding="UTF-8"?>
  <Authentication username="testuser" password="ECLPASS"/>
  <Hotel id="411"/>
  <AvailRateUpdate>

<Authentication username="testuser" password="ECLPASS"/> this line but add new noad hotel  then it can be inside of  
<authentication username="testuser" password="ECLPASS">
  <hotel id="411" />
  </authentication>

How to solve this
or how to create hotelid after the authentication completes


my code below
  XmlTextWriter writer = new XmlTextWriter(Server.MapPath ("product.xml"), System.Text.Encoding.UTF8);
        XmlDocument doc = new XmlDocument();
        writer.WriteStartDocument(true);
        writer.Formatting = Formatting.Indented;
        XmlNode AuthenticationNode = doc.CreateElement("Authentication");
        XmlAttribute UserName = doc.CreateAttribute("id");
        UserName.Value = "eqcuser";
        XmlAttribute password = doc.CreateAttribute("Password");
        password.Value = "eqcpass";
        AuthenticationNode.Attributes.Append(UserName);
        AuthenticationNode.Attributes.Append(password);
        doc.AppendChild(AuthenticationNode);

        XmlNode root = doc.CreateElement("Hotel");
        XmlAttribute  HotelNode = doc.CreateAttribute("Id");
        HotelNode.Value = "36972";
        root.Attributes.Append(HotelNode);
        doc.AppendChild(root);