1.Suppose that Rosa and Clara are spending their entire budget on candy and movie tickets. Their utility function over candy, C, and movie, M is U = 2 C M. Their marginal utility from candy is MUC = 2 M, and their marginal utility from movie is MUM = 2 C. A bag of candy costs $5 and movies cost $10 per ticket. Each has budget of $80 to allocate to candy and movie tickets. If they maximize their utility, what would be their optimal bundle -- how many candy bags and movie tickets would they buy? Show the results on a diagram with a budget line and indifference curve. You must show all your work and you must be very precise with the intercept values on the diagram showing the maximum amount of candies and movie tickets they can buy.

2.Now suppose that their new budget to be spent on candy and movie tickets is $100. Show this change on a new budget line. If they maximizes their utilities, solve for their optimal bundle and show this bundle in a diagram using indifference curves and a budget line. Explain your results.

3. Suppose that they still have $100 budget to spend on candy and movie tickets. However, it costs them $10 to buy a bag of candy and it costs $10 to buy a movie ticket. Show this change on a new budget line. If they maximize their utilities, solve for their optimal bundle and show this bundle in a diagram using indifference curves and a budget line. Explain your results.