1. Consider a module with the following marking scheme: There are two tests and your overall grade is equal to the minimum of your grades on the two tests. So, for example, if you score 88 on test 1 and 34 on test 2, your overall grade in the course is 34. (c) Suppose that a student has the utility function, U(G, M) = G - -M2 where G is the student' s overall grade, M is the number of minutes the student spends studying, and A > 0 is a parameter that reflects how much the student dislikes studying. For this student, find the total amount of study time (M) that maximizes utility. (Hint: use your answer from part (a) and take a first-order condition). (d) Continuing with part (c): If a student chooses the utility-maximizing amount of study time and allocates this most efficiently between the two tests, then what will be the overall grade in the course? Your answer should depend on the parameters, A, p1 and p2 (e) Roy has a utility function like the one above, and for him, p1 = 5, p2 = 15 and A = 36.000 . If Roy chooses his total study time to maximize utility, how many total minutes does he spend studying and what will be his overall grade in the course