Ronald is an Economics students who likes to spend his leisure time of sixty hours a month doing one of two activities: watching movies at Dendy Cinemas Newtown (:3), and indoor-climbing (y). A trip to the movies takes 3 hours, and each visit to the climbing gym lasts 5 hours. Further, suppose that Ronald has a xed monthly monetary budget to spend on leisure activi- ties He currently exhausts this entire budget by watching two movies and visiting the climbing gym fteen times. With this monthly budget, he would also have been able to afford exactly seven movies and six visits to the climbing gym. Assume that both goods are perfectly divisible. Continue to consider Ronald from Question 2. Suppose that Ronald's preferences over movies and climbing are such that he likes them exactly equally: he is always willing to trade one movie for one climbing session and remain exactly as well of as he 1was before. One valid utility representation of Ronald's preferences is u(m, y) = :r + y. (d) i. Explain Why,r Ronald's optimal consumption bundle must lie on the outer boundary,r of his budget set. ii. Identify Ronald's optimal bundle by visual inspection. Briey explain what you did. iii. Find Ronald's optimal consumption bundle using a mathematical argument