How to use convex hull for this problem
Perhaps you want a hint first?
Of course you start by considering all vectors $(a_i,b_i)$ first. The vector $(a_i,b_i)$ indicates the amounts you earn by working one hour on job $i$.

What is the meaning of any point on the line segment between points $(a_i,b_i)$ and $(a_j,b_j)$? 

If any point $(a_k,b_k)$ is within the triangle $(0,0)$, $(a_i,b_i)$, $(a_j,b_j)$ why can you discard it?