XYZ Manufacturing produces bicycles using a multi$-$step process:

Frame Welding: $15$ minutes per frame

Wheel Assembly: $10$ minutes per wheel

Painting: $25$ minutes per bicycle

Final Assembly: $30$ minutes per bicycle

The welding machine requires a setup time of $20$ minutes for each batch of frames, and the painting station has a changeover time of $30$ minutes between different colors. XYZ operates for $8$ hours per day. What is the capacity of the welding machine $($in bicycles per day$)$ if the batch size is $40$ frames?