PowerPivot DAX case: Resouce planning report with selecting a date parameter

I had an interesting question on my ask a questions page, one that I have (or something similar) heard a few times before. So I decided to do make a blog post on how to solve it

Our company tracks changes in the resource planning using a data warehouse. An example would be: Assignment 1: Ian 8 hours planned for 3-Jun; valid from 1-jan-2011 until 1-feb-2011. Assignment 1: Ian 6 hours planned for 3-Jun; valid from 2-feb-2011 until 15-feb-2011. Assignment 1: Ian 7 hours planned for 3-jun; valid from 16-feb-2011 until infinity. I what to enable our end-user to select any date level (Date, Week, Month, year) and get the current planning for that planned date (3-jun).