Programmatically add product to cart [WooCommerce & Product Add-ons]

I am using WooCommerce and have setup my products with the Product Add-ons plugin (https://www.woothemes.com/products/product-add-ons/).

Is there a way to programmatically add a product to the cart which has addons (from a non woocommerce page)?

So far I’ve been able to add the raw product with no addons using this ajax call for a product with an id of 28:
$.post(‘/wp/?post_type=product&add-to-cart=28’;

This adds the product to the cart with no addons but if I want to pass the addon variables, how can I do that?