Please guide me

1.)The utility function of consumers is represented as U = :L0X"'5YIn with X and Y as two outputs in the consumer's basket. Marginal utility from output X is MUx = 5X'D'5Y0'2 while marginal utility from outputY is MUy = 2X'5Y''8. Consumer's income is 100,000 while the prices of output is given as Px = 1 while Py = 2. Use the information provided in this item to answer the following questions. i.)What is the consumer optimal condition (MRS = MUXI MUy = Px / Py )for the consumer? What is the relevance ofthis optimal condition for the consumer? ii.)What will be the optimal combination of output X and Y given that consumer's income is 100,000 and the price of output X is PK 2 1 while that of output Y is R, = 2? iii.)A price ceiling was imposed on output Y such that P ' = 1. What will be the new consumer optimal condition given this change in the price of output Y? iv.)What will be the new optimal combination of outputs X and Y given the change in the price ofoutput Y? Do you agree that the imposition ofa price ceiling will increase quantity demanded for output Y? Answer yes or no but justify your answer using the information provided in this item