They are bound to take the most economical offer which is not necessarily the cheapest. Cost must always be a significant factor but others can be included. The criteria must be fixed before starting the process and can include follow-up cost, technical aspects, environmental considerations, duration, user experience, or anything else that is quantifiable, appropriate, and non-discriminatory.

It is far easier to just look at the cost but it's absolutely not uncommon to have other criteria included in a tender.

An offer that is unusually cheap has to withstand additional scrutiny. It is not allowed to choose such an offer (even if it's the cheapest) if it's price-dumping or unlikely to be completed due to the tight calculation.