To find the total number of tickets sold for the production, we can set up an equation based on the information given. The tickets sold for Friday night (405) represent 45% of the total tickets sold.
Let \( x \) be the total number of tickets sold. We can express the relationship as:
\[ 0.45x = 405 \]
Now, we solve for \( x \):
\[ x = \frac{405}{0.45} \]
Calculating the right side:
\[ x = \frac{405}{0.45} = 900 \]
Thus, the total number of tickets sold for the production is \( 900 \).
The correct answer is \( \boxed{900} \).