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Using a third party API to get prices of products after user configuration

I’m a printer shop reseller,
and I have a wordpress/woocommerce store with YITH product add-ons.
every product has more or less then 7 options to choose from.
The customer can choose the product he wants and then choose from the options.

The problem : is that the prices are very "random", not every option has a specific amount of money.
For ex : if you choose a paper size A4, the price of printing the both sides is 1$.
but if you choose paper size A5, the price is 5$, and if you choose a specific type of paper the price of printing the both sides is 19$ -_-.

So i must use the API of my supplier to get the prices,

Here is the API doc link : https://media.realisaprint.com/documents/rea-api/2.1/api_realisaprint_com_v2_1.pdf

How to do it :
I will get all the options and send them via the a post request via an URL and show the results (JSON).

But i don’t know how to do it technically,
can use hooks and filters in my functions.php ? if yes which hook ?

can any one make any suggestions to explore ?

Thank you very much.