Robin likes to watch movies in her spare time. She can watch: (i) movies at the cinema (x) (ii) movies at home ( y) Robin has 24 hours of spare time a month. Going to the cinema takes up to 4 hours, while watching movies at home takes only 2 hours. Robin is not too picky about the choice of movies except that she does not like to watch the same movie twice. Each month, Robin can spend up to $160 to spend on movies. Going to the cinema costs $20. Watching movies at home requires paying $10 per movie. (a) Write down Robin's budget constraint and time constraint. (b) Draw Robin's budget constraint and time constraint in a clearly labelled diagram. Label all axis intercepts in the two axes (x and y). Shade the set of bundles that Robin can afford ( those satisfying both her time and money constraints) with vertical lines (c) A movie is a movie. Nonetheless, Robin likes to watch movies on the big screen at cinemas. In fact, she likes to watch any movie at a cinema thrice as much as she likes to watch a movie at home. Her preference is given by the utility function: U = 3x + y Let (x*, y*) denote the bundle that maximizes Robin's utility subject to constraints faced by Robin. Find (x*, y*). Show your mathematical working out. (d) Post Covid, the price of going to the cinema has gone up from $20 to $40. Assume that the time and monetary cost of watching a movie at home has not changed. Robin's preferences and budget have not changed either. Find the new utility maximizing bundle for Robin. [Hint: While the question is about how part (c) changes with new information, look at how parts (a) and (b) change first. That will help in answering part (d)].

• Please don't use ai and explain in detail with formula and calculations