A scientist developed an early diagnostic test for a disease. The test has false positive and false negative rates both equal to 1%. The prevalence of the disease in the population is 1 out of 5000. If the disease is not diagnosed early, the treatment will cost $25, 000. If it is diagnosed early, there is a preventative treatment which costs only $125. Assume that everyone whose test came out to be positive will undergo that preventative treatment. Also assume that every diagnosis will be an early diagnosis. Required:
Advise the scientist on the maximum price of a diagnostic test, such that it is still cheaper to test everyone than not to test anyone.