
Hi Lucy, just plot the level curves for this function with some constant c = max{L,K}. On plotting you will find that the level curves are mirror image of inverse L shaped curves and the convex set is the lower level set not the upper level set.
And also Since L and K are linear functions thus they are both convex and concave functions but Q(L,K)=max(L,K) is a "Convex function" not "Concave function"!
