Figure ?? shows a myopic function INFORMATION-GATHERING-AGENT(t) returns hat chooses the next evidence variable to observe according to the ratio VPI(E_j)/C (Ej), where C (E_j) is the cost of observing E_j. The optimal algorithm for the treasure-hunt problem ranks the prospects according to P(E_j)/C (E_j), where P(E_j) is the probability that the treasure is in location j. 

a. Calculate VPI(E_j), assuming the treasure is valued at v. 

b. Determine if the two algorithms give the same behavior for the treasure-hunt problem. 

c. Does the value v matter? Explain how to incorporate it into the treasure-hunt algorithm and give a proof of optimality for the new algorithm.