please solve it in 20 mins I will thumb you up please I need hand written solution please fast I will give you good comments also

Chloe sets aside a budget of 100 for spending on fashion accessories ( goodX) and cosmetics ( good Y ), the prices of which are PX=50 and PY=25, respectively. Chloe's preferences over the two goods are described by the utility function U(X,Y)= XY, for which MUX=Y and MUY=X. (a) Explain how Chloe's preferences can be translated into indifference curves. Sketch some of these in a diagram. Do her indifference curves touch the axes? [7 marks] (b) Find the number of fashion accessories and cosmetics that Chloe chooses to consume and illustrate her choice in your diagram. [8 marks] (c) Chloe invites her closest friends to celebrate her birthday and receives 8 fashion accessories as gifts, but no cosmetics. What is her utility gain from these gifts, assuming Chloe starts from the bundle in (b)? Add Chloe's new bundle and corresponding indifference curve in your diagram. [5 marks] (d) Analyse whether Chloe would be better off receiving a gift voucher equivalent in value to 8 fashion accessories, but which she can spend as she likes. Do you find this model a good description of the enjoyment from receiving birthday gifts? [10 marks]