WordPress Custom Post Types Class

My custom post type doesn’t seem to be pulling through to the admin dashboard. I have done it as a plugin and have activated it but to no avail. Shouldn’t it show up down the left hand side? I also cant seem to find any errors in the code

<?php
/**
 * Plugin Name: Production.
* Description: Create a new production for your website.
*/

class Production {


function __construct(){

    add_action( 'init', 'my_custom_post_product' );
}


function my_custom_post_product() {
    $labels = array(
        'name' => _x('Productions','post type general name'),
        'singular_name' => _x('Production','post type singular name'),
        'add_new'            => _x( 'Add New', 'Production' ),
        'add_new_item'       => __( 'Add New Production' ),
        'edit_item'          => __( 'Edit Production' ),
        'new_item'           => __( 'New Production' ),
        'all_items'          => __( 'All Productions' ),
        'view_item'          => __( 'View Production' ),
        'search_items'       => __( 'Search Productions' ),
        'not_found'          => __( 'No productions found' ),
        'not_found_in_trash' => __( 'No productions found in the Trash' ),
        'parent_item_colon'  => '',
        'menu_name'          => 'Productions');

    $args = array(

        'labels' => $labels,
        'description' => 'Holds the productions',
        'public'        => true,
        'menu_position' => 5,
        'supports'      => array( 'title', 'editor', 'thumbnail', 'excerpt', 'comments' ),
        'has_archive'   => true,

    );

    register_post_type( 'Production', $args );

}


}