3. Dune (water rights) Arrakis is a planet without much water. There are two uses for water: consumption by local inhabitants, which creates local utility u ( w ) = 8 w 12 w 2 for w units of water, and spice mining, which creates profits ( w ) = 4 w 12 w 2 . (a) Suppose that we care equally about utility and profits and that there is a total of w = 4 units of water on Arrakis. What is the first-best allocation of water