Hiring one more assistant increases the time available for stitching buttons and button holes.

Max. No. of shirts those cutter can cut for JASMINE in a day = $\frac{1200}{20}$ = 60

Time required by Tailors to stitch 60 shirts = (60 $\times$ 60) = 3600 mins, whereas time available is

3000 mins only.

Hence maximum No. of shirts that can be stitched in a day = $\frac{3000}{60}$ = 50

Time consumed by assistant to stitch buttons to 50 shirts = (50 $\times$ 50) = 750 mins

Time available for assistant = (3 $\times$ 10 $\times$ 60) = 1800 mins.

Hence 50 shirts can be completed in a day.