PHP for Vitelity API for DID Reservation and Order

We are a VoIP Service provider, and we use Vitelity to purchase DID phone numbers for our customers. Vitelity offers an API we can use where our customers may view available DID phone numbers through our website, be able to select any available phone numbers, and reserve them so we can purchase the numbers for them. I would like to implement this API along with a complete customer order, account set up, pricing details, product cart, and checkout page. Here is a link to the Vitelity DID information: [login to view URL] and here is another link of a company that uses Vitelity API on their website https://store.phonebooth.com/pb/store#cart_id=1cb7b99d-292b-3b53-3cb1-45b5b6dcc272