Suppose students have to take an exam with n questions. the time for the exam is no more than t minutes. the score on each question, si, depends on how good is the answer to that question, with a maximum score of si*. scores depend on a production function of performance for each question that depends on time put into that question, and the knowledge, k, brought to the exam.
a. suppose the grade, g, depends on the sum of the si, and that utility is equal to g. how much time would a person allocate to each question? how does that depend on k and the production function for each question?