Solution with $xy \to 5000$.
To maximise the volume in the water, choose a material that has the same density as water, and place it so that the top face sits at the surface of the water. Having equal density with water means the object won't rise or sink. This allows $x$ to approach 100.
To maximise the surface area above the water, choose a short shape with one large face. An extremely shallow pyramid would allow $y$ to approach 50. (I'm ignoring the effects of the water's surface tension.)
Water density varies with temperature, with a peak of 1000 kgm$^{-3}$ at 4$^\text{o}$C. At 80$^\text{o}$C, the density of water is 971.8 kgm$^{-3}$, which is close to sodium's 970 kgm$^{-3}$. (Don't actually put a slab of sodium into hot water, though!)
Plastics come in a variety of densities, with Polyethylene Polystone M-Flametech said to have a density of 0.98 g/cm$^3$, or 980 kgm$^{-3}$. A slab of this material should do the trick with the water somewhere between
60$^\text{o}$C and 80$^\text{o}$C.