An exam consists of four questions. If Adam spends time ti on Question 2', he expects to receive mark w; (1 e'ti/ 31'), where 1111- > 0 is the number of marks assigned to Question 1', and 52' > 0. The total time length of the exam is T. (a) [5 marks] How does Adam's expected mark from Question i depend on Bi; is it increasing or de- creasing in 31-? What is an intuitive meaning of the parameter 52'? (b) [5 marks] Formulate Adam's problem of the optimal time allocation (among the four exam questions). His goal is to maximise his expected mark from the Whole exam. (0) [5 marks] Show that Adam's problem always has a solution