Professor Myers teaches the course 'Extraterrestrial Biology' for the first time in the academic year 2020/21. When it comes to making the exam, she has to decide on the number of multiple choice questions (a) and the number of open question (y) to include in the exam. Her objective is, to design the exam in a way that will assess and evaluate the knowledge of the students in the best possible way. Based on her extensive teaching experience, she estimates that the level of accuracy of the student grades is related to the number of multiple choice question (a) and the number of open questions (y) as described by the function A(x, y) = 100 (6x2 + 2y2 + 60xy + 60x + 900y). Where 0 is the lowest possible accuracy level (equivalent to giving random grades) and a higher score stands for a higher accuracy of the exam. The length of the exam is 2 hours. From experience with similar courses, professor Myers knows that a multiple choice question takes a student approximately 4 minutes to solve, and an open question takes 20 minutes. The exam should be constructed in a way that allows to solve all questions within the time limit. This leads to the constraint 4x + 20y = 120. Solve the following constrained optimization problem: How many questions should Prof. Myers pose of each type to achieve the highest possible accuracy level for her exam