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. (a) Suppose that a student who spends no time studying for a test receives zero marks on that test. Suppose that each mark received on test 1 costs p1 minutes of study time. Each mark received on test 2 costs p, minutes of study time. Consider a student who spends a total of M minutes studying for the two tests and allocates this time most efficiently to achieve the highest overall grade. What will be this student' s overall grade? (your answers should depend on M , p, and pz) (b) If a student wants to achieve an overall grade of G with the smallest possible total time studying, how much time must the student spend studying on test 1? How much time must the student spend studying on test 2