The Maryland Department of Corrections has just implemented a new policy for the prescription of drugs to treat Hepatitis C in its prisons. Under this policy, all prisoners who are infected with the Hepatitis C virus must be treated. Each year for each prisoner, the provider must decide one of two dosages of medicine to prescribe. The cost of treating with a low dose is 150 dollars per year and the cost of treating with a high dose is 200 dollars per year. In each year the probability of cure is independent of that in other years. The probability that treatment will be successful (the disease will be cured) in a given year is .2 under the low dose regime and .5 under the high dose regime. Hepatitis C is not deadly, so any uncured prisoner remains in prison for the duration of their sentence (time left to serve).

a) What is the minimum expected cost treatment plan for treating a prisoner with two years remaining on their sentence? (Round your answer to 0 decimals.)

b) What is the minimum expected cost treatment plan for treating a prisoner with three years remaining on their sentence? (Round your answer to 0 decimals.)

c) If there are 100 prisoners with Hepatitis C who have two years remaining on their sentences and 100 prisoners with three years remaining on their sentences, what is the minimum expected total cost of treating all 200 prisoners?

d) Suppose now that you are told you have a budget of $62,000 to treat all 100 prisoners with Hepatitis C who have two years remaining on their sentences and 100 prisoners with three years remaining on their sentences. What is the optimal number of 3 year-left prisoners who will receive a high dose of treatment every year that maximizes the average number of prisoners cured? (Your result should be an integer.)