Julia has strictly convex preferences and she allocates all of her income to the purchase of good X and good Y. At her current income of $3000 per month, with price of X being $20 per unit and price of Y being $35 per unit, Julia chooses to allocate her income equally between the two goods. What quantity of X does she purchase? Show your working. What quantity of Y does she purchase? Show your working. Part (c) Represent her optimal bundle on a diagram by employing all the relevant tools such as her indifference curve and her budget constraint while keeping good X on the horizontal axis. Briefly explain your work. Suppose that price of good Y falls and at the same time Julia's income also changes in a way that she is exactly as well off after these changes as she was in part (b). Do further work on your diagram for part (b) to show an appropriate position of Julia's new budget constraint which is consistent with this observation and also show an appropriate location for her new optimal bundle. Explain your work. Will an income effect be induced due to these changes? Explain your stance.