Change product price for individual sales

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Hey!
Me and my friend are wanting to start a business where people can order custom PCs, based on the parts they want we will build it and then ship it to them.
I want our website to allow the user to go through and pick out their parts, and then the price of their PC will be calculated based on what parts they picked (essentially having to create a unique "product" with it's own price for each order).
Is this possible through one of the Shopify API's. If so which one and how?