Optimizing a physician's medical test plan I have come across the following optimization problem:

"A patient presents himself with symptoms to a physician. The physician has a set of $n$ medical tests, where each test $i$ has costs $c_i$ associated with it and returns a perfectly reliable result (usually positive/negative). The physician can perform these medical tests to decide which medication to prescribe. The physician knows rules like
  
  
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*If test A is positive and test B is negative, prescribe medication X.
  
*If test C is positive, also prescribe X.
  
*In all other cases prescribe Y.
  
  
  Given these rules and the costs of all the tests, which sequence of medical tests should the physician choose in order to minimize the expected treatment cost?"

Unfortunately, I have a hard time finding any information about this problem. Is there a specific name I can google for? Or alternatively, can someone point me to a mathematically rigorous formulation?
Basically, I would like to do a literature review on this problem, but with all the economic debates about medical costs and insurances its pretty hard to find anything on the Web. 
 A: As @lewellen points out, this can be modeled by a Markov Decision Process. The state space is the cross product of all different test outcomes (e.g. for three tests which can be positive/negative each, we can encode the state space as a triary string of length 3: test is positive, negative or not yet taken). The actions correspond to performing a test, and the outcome of the test determines in which state we end up after following said action. Every action is associated a reward equal to the negated cost of the medical test performed. Entering the states in which the physician (according to the rules) knows which medication to prescribe is given a large enough reward (so that reaching these states is lucrative). The initial state is the state in which the outcome of all tests is unknown. The objective is then to find a strategy that maximizes the expected reward.
As @AlexBecker points out, the optimal strategy depends on the prior probabilities that a certain test will be positive. Optimally, the joint probability distribution over all test outcomes is given.
