What shape is the long-run aggregate supply curve? Why does it have this shape?

Given in the question that, the long-run aggregate supply curve.

According to neoclassical economists, potential GDP is the preliminary determinant of actual GDP, and the LPAS curve is pointed at potential GDP. In the AD/AS model, potential GDP is displayed as a vertical line, and thus the LRAS curve is a vertical line as displayed in the below graph, sketched at the level of potential GDP totality output level, With time, the LRAS curve shifts rightwards as productivity boosts and potential GDP expands and in the long run, the aggregate supply curve does depend on the elements of production and not on costs.

The long-run result doesn't depend on the costs but the elements of production.

Hence, the shape of the long-run aggregate supply curve is vertical.