(Challenge) Raisins

Chef Ada baked a rectangular cake with width $W$ and height $H$. To finish the cake, she placed $R$ raisins on it. For simplicity, we will represent raisins by points in a plane. For each valid $i$, the position of the $i$-th raisin is $(X_i, Y_i)$. The price of the cake is twice the area of the smallest convex polygon that contains all raisins. Ada thinks that the current price is too high, so