Many colleges face the problem of drug testing for their athletes. Assume we are concerned with the following costs:

c₁ = cost if an athlete is falsely accused of using a drug.
c₂ = cost if an athlete cannot be accurately identified as a drug user.
c₃ = cost due to invasion of privacy if a nonuser is tested.

Suppose 5% of all athletes are drug users and that the preferred test is 90% reliable. This means that if an athlete uses a drug there is a 90% chance that the test will detect it, and if the athlete does not use drugs there is a 90% chance that the test will show no drug use. Under what conditions should the college test for drugs?