class MyProducer
{
  ....
}

Model model = new Model();
var q =
    model.Products
    .Select(
      p =>
        new
        {
            id = p.Id,
            producer = p.Producer != null ? new MyProducer { id = p.Producer.Id } : null
        });

var r = q.ToArray();

using(var model = new Model())
{
    var q =
    from product in model.Products
    join producer in model.Producers.DefaultIfEmpty()
    on product.ProducerId equals producer.Id
    select new
    {
        Id = product.Id,
        Producer = producer != null ? new MyProducer{ Id = producer.Id} : null
    }
}

Model model = new Model();
var q = model.Products.Select(p => new { id = p.Id, producer =
    p.Producer != null ? new Struct { id = p.Producer.Id } : (Struct)null });

var q =
    model.Products
    .Select(p => new
        {
            id = p.Id,
            producer = new MyProducer
            {
               id = p.Producer == null ? 0 : p.Producer.Id
            }
        }
     );

var r = q.ToArray();