Hello could i have some help with this questions struggling to solve it

Question 1 Charlotte spends her income of $241113 on clothing (good x}, and the composite good (good y]. The utility Charlotte receives from consuming a basket of clothing and the composite good is, Y , = 2 . U[x y) + Bill) The corresponding marginal utilities are, 1 1 MUX T? and MU}; REQUIRED: (a) Is the 'principal of diminishing marginal utility' satisfied for both clothing and the composite good? Brieflyr explain. [2 mark) (h) Derive an expression for Charlotte's marginal rate of substitution. Is the marginal rate of substitution diminishing? Briefly explain. {2 marks) (c) Find Charlotte's optimal consumption basket when the price of clothing is P\" = $52G, and the price of the composite good is P}. = $1. (3 marks) (d) Find Charlotte's optimal consumption basket Iwhen the price of clothing increases to PX; = $60 (the price of the composite good remains 1F\"F = $1}. {3 marks) (e) Find the income and substitution effects for the price increase. ls clothing a normal good? Briefly.r explain.