To find out how many pita sandwiches are made per day, we need to divide the total number of sandwiches by the number of bread types.
The sandwich shop offers 4 types of bread, and they produce a total of 364 sandwiches each day.
Thus, the number of sandwiches made with each type of bread is:
\[ \text{Number of sandwiches per type of bread} = \frac{\text{Total sandwiches}}{\text{Number of types of bread}} = \frac{364}{4} = 91 \]
Therefore, the number of pita sandwiches made per day is:
\[ \boxed{91} \]