I Can Use Both Hands!

Chef has a special ability: he can use both his left and right hands equally well, and at the same time! To put this ability into practice, Chef decides that he's going to write a novel with his left hand, while writing code with his right. Chef needs $L$ minutes to write a page with his left hand, and $R$ minutes to write a line of code with his right. Chef defines his *satisfaction* to be th