I have to determine the worst case values for R3 and R4 to provide an LED current of 50 mA. I don't even understand the question, what would constitute worst case? Help would be appreciated.

Cheers

 

A worst-case design assumes that all component characteristics have their least favourable values.

Assuming that the transistor is supposed to saturate, to find the transistor base resistor you could assume that the transistor has the minimum value for gain HFE(sat), and the maximum value for Vbe, if available. The IC should be taken to have the minimum high-level output voltage.

The calculated base resistor value should be taken to be at the highest tolerance limit, so the actual (preferred) value should be chosen accordingly.

The worst-case for the LED ballast resistor will depend whether 50mA is a minimum or maximum requirement. You need to consider the LED Vf and the transistor VCE(sat).