The formula to calculate the number of posts is:

\[ \text{Number of Posts} = \frac{\text{Fence Length (ft)}}{8} + 1 \]

The formula to calculate the total number of rails is:

\[ \text{Total Number of Rails} = \left( \frac{\text{Fence Height (ft)} \times 12 - \text{Top Gap (in)} - \text{Bottom Gap (in)}}{\text{Rail Height (in)} + \text{Rail Spacing (in)}} \right) \times (\text{Number of Posts} - 1) \]

The formula to calculate the amount of cement bags is:

\[ \text{Cement Bags} = \begin{cases} 3 & \text{if } \text{Fence Length} < 9 \\ 4 & \text{if } 9 \leq \text{Fence Length} < 19 \\ 5 & \text{if } 19 \leq \text{Fence Length} < 29 \\ \lceil \frac{\text{Fence Length}}{10} \rceil + 2 & \text{if } \text{Fence Length} \geq 29 \end{cases} \]