It is very difficult to estimate custom integrations. One product custom integrations through apps have been done for less than $1,500 however these can also be very expensive depending on the complexity. If the integration involves a system with an open API the amount can be reasonable however when it involves a integration with a system like VendorNet there can be significant expenses.
Since we want to partner with you to enable your creative idea we would love to have a conversation about the least expensive way to get this launched.
We call this CIEP and until we have a conversation and develop an understanding of what you are trying to accomplish we cannot even guess how long this will take. It could be four weeks to four months. We did complete a "papercliped" integration in 2013 in less than two weeks because the client was in significant trouble and asked real nicely.....
Please email firstname.lastname@example.org to schedule the initial conversation to see if we are a fit for your goals.