How to predict the maxima and minima of a tidal wave? Assume that a planet of mass $m$ and radius $r$ is orbiting a massive star of mass $M$ at a orbital distance $R$. Assume that the planet is covered in a ideal, non viscous ocean on a friction less surface. Hence the ocean will align itself along the equipotential surface generated by the two masses. Let the maximum height of the water bulge from the planet's surface be $H$ and minimum height of the water bulge be $h$.

What are the mathematical relations between the above values?

My effort at a solution
I found a related question on Physics SE. It references Hale Bradt, Tidal distortion: Earth tides and Roche lobes which is too complex for me too understand.
It would greatly help me if someone can simplify the article and present me with the formulas connecting the above quantities (without proof if needed).
I am a high school student and I need this for a Olympiad Problem which I am trying to solve.
I understand Olympiad level Physics and Astronomy.

Equation 20 in that article seems to provide what you are looking for. It describes the displacement (from spherical) of the equipotential at the surface of the planet (where $\phi$ is the polar coordinate with 0 pointing towards the other mass) .
Using the terms you have defined the equation is
$$ dr=\frac{m} {M} \frac{r^4}{2 R^3} \left( 3 \cos^2 \phi - 1\right) $$
The maximum bulge will be towards the star 
$$dr(\phi =0) = H = \frac{m} {M} \frac{r^4}{R^3} $$
While on the perpendicular axis the sphere will be flattened
$$dr(\phi =90^\circ) = H = - \frac{m} {M} \frac{r^4}{2R^3} $$
You can see in that article how they have used this to calculate the 54cm value for earth tides.
To get the actual radius of the planet at a particular position you would add dr to r. 
