Metabox does not show in custom post type

The custom post type is being register as name, not snippet as is being called in add_meta_boxes action. This is because a PHP var is passed inside single quotes and it is not being interpreted.

Change this:

register_post_type('$name', $args);

To:

register_post_type($name, $args);

This also work:

register_post_type("$name", $args);

But never pass PHP variables inside single quotes if you want they be interpreted.

Also, it is recommended the use of add_action('add_meta_boxes_{post-type}', 'callback') to create less unnecessary hooks for other post types (from codex).