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Amy loves fancy and fashionable outfits. She never wears an outt twice. She has a utility function takes the form \"(5.3) = XI/zyi = \\lggg, where x stands for the number of "new outts" and y is the amount of "Other goods\" essential to her living. That is to say, Amy's marginal utilities for new outt and other goods are: MUX=EJ 1 Respectively. Amy recently noticed that one of her favourite brand'Supreme\" is offering a deal on its' latest patchwork hooded jackets, which is sold at $100 a piece. The promotion claims that one can "get the second piece 50% off.\" It means, if Amy buys a jacket from Supreme for $100, she can buy the second jacket (of different colour} for 50% of the original tag price, $50. In addition, if Amy wants a third jacket, she has to pay 5100 again, but now she has the privilege to purchase the fourth jacket for 550, etc. Assume the price for \"Other goods\" is $50 and Amy has a monthly income of $1,000 to spend on both the Supreme jackets and \"Other goods.\" Answer the following questions. Note that, if your final results are not integers, report the results up to two decimal digits. (c) Based upon the information given, what is Amy's optimal consumption bundle? What is her utility level at this optimal bundle? Show your work with necessary details. (cl) If Supreme announces a different promotion scheme: instead of "get the second piece 50% off," the store offers a 25% off for every jacket sold, would Amy be better off, worse off, or indifferent between these two promotion schemes? Show your work with necessary details.|