Suppose a student has no more than t minutes to write an examination consisting of two questions, 1 and 2. He receives A points if he gets question 1 correct and B points if he gets question 2 correct. He knows that if he spends s minutes in question 1 (assume he uses up all his time), then
1) the probability that he gets it correct is p(s)
2) the probability that he gets the second one correct is q(t-s).
Both p( ) and q( ) are strictly increasing and concave functions. In addition, assume there is no partial credit, and the student receives constant marginal utility for additional points.
(Question a) Derive the equilibrium conditions for his optimal allocation of time between the two questions.
(Question b) How is his allocation a acted by a change in A or B?