What is use of R41 (base to emitter) resistor in Transistor Relay Circuit?
It prevents leakage through the optoisolator from partially turning on the transistor. 

Find the maximum leakage of the opto (typically it will occur at the maximum junction temperature ever expected) and calculate the resistor to drop no more than something like 0.4V. Then go back and make sure that it's not hogging too much base current under worst-case (low) CTE etc. 

That particular opto has 1uA typical leakage at Tj=100'C, so you might want to allow for 3-10uA worst-case. 

I can't read the values there very well, but typically R3 and R41 about the same value works, and if that is actually 115K, it looks way too high to reliably drive a relay, especially considering the relatively poor guaranteed gain of the MMBT2222.