The final exam is coming soon. The exam consists of two parts, i.e., part A and part B. There are a total of QA and QB questions in parts A and B, respectively. As a student, you only care about the total combined marks you receive from all the correct answers from part A and part B. Each correct answer from part A and part B is worth A and B marks, respectively. It takes you A minutes to correctly answer one question in part A and B minutes to correctly answer one question in part B. For any question that you attempt, you will get some marks depending on the time spent on the question. For example, if you spend 0.2A minutes to answer one question in part A, you will receive 0.2A marks. Let qA be your total correct answers from part A, and qB be your total correct answers from part B. The total duration of this exam is M minutes. Apply the consumer optimisation model to this problem.

(e) Now, suppose that QA = QB = 10, A = 3, B = 2, A = 5, and B = 4. (i) (5 marks) Suppose you need to achieve at least 50% of the total maximum marks to pass this exam. If you want to just pass the exam, what is the shortest time that you need to spend on this exam?