Defective-Batch Inspection With an Imperfect Detector

A batch is defective with prior probability $\frac14$. Accepting a good batch pays $+20$; accepting a defective batch pays $-40$; rejecting pays $0$. Before deciding you may run a detector that flags 'defective.' It flags a truly defective batch with probability $\frac{9}{10}$ and a good batch with probability $\frac15$ (false positive). What is the value of running the detector (the increase in expected payoff from using it optimally)?