Could you please provide step bu step solution?

Suppose that consumers are always using 2 units of X and 6 units of Y in fixed proportion. a-) (8 points) For the above utility function, derive the demand functions for X and Y as functions of prices and income. Explain whether these goods are normal goods. Explain whether two goods are complements or substitutes. b-) (6 points) Suppose now that Price of good Y is $12 and income equals 1200. Using three distinct values of price of X (PX = 6, PX = 12, PX = 24). draw Price consumption curve and then using Price Consumption curve draw the demand curve for X. c-) (6 points) Suppose Price of good Y is $48 and price of X is equal to 6. Using three distinct income values ( 10 =1200, 1] = 2400 , 12 = 3600), draw Income Consumption curve and then using Income Consumption curve draw the Engel curve for good X. d-) (8 points) Consider initially that Income (1) = $1200. Px -6 and Py =12. What is the initial optimal consumption levels of X and Y? Suppose that Px rises from $6 to $12. Find the substitution effect, income effect and total effect on good X. Explain the steps carefully and support your result with an explanation and a graph. A/