DE-MO 2018 Problem 4

a) Let $a,b$ and $c$ be side lengths of a triangle with perimeter $4$ . Show that $$a^2+b^2+c^2+abc<8.$$ b) Is there a real number $d<8$ such that for all triangles with perimeter $4$ we have $$a^2+b^2+c^2+abc<d$$ where $a,b$ and $c$ are the side lengths of the triangle?