The cost per submarine, $y in millions, of assembling $x$ submarines can be modelled by
$y = \frac{5}{2}x^2 - 20x + 100$
where $x \le 8$.

1. Interpret the constant term in the context of the model

The constant term $100$ corresponds to the value of $y$ when $x = 0$. In the context of the model, this represents the theoretical base cost per submarine (in millions of dollars) before any economies of scale from assembling multiple submarines take effect.

1. Factor out the coefficient of $x^2$ from the first two terms

$y = \frac{5}{2}(x^2 - 8x) + 100$

2. Complete the square inside the bracket and simplify

$y = \frac{5}{2}\left[ (x - 4)^2 - (-4)^2 \right] + 100$
$y = \frac{5}{2}\left[ (x - 4)^2 - 16 \right] + 100$
$y = \frac{5}{2}(x - 4)^2 - 40 + 100$
$y = \frac{5}{2}(x - 4)^2 + 60$

1. Interpret the significance of the vertex $x = h$ in the context of the quadratic model

Since the coefficient of $x^2$ is positive ($a = \frac{5}{2} > 0$), the quadratic function has a minimum value at $x = h$. In the context of the model, $x$ is the number of submarines assembled and $y$ is the cost per submarine. Therefore, $x = h$ is the number of submarines assembled that results in the lowest possible cost per submarine.