Show work please

Ellie's preferences are described by the utility function U = 4DT, where D indicates the quantity of donuts and T is the quantity of tea. The price of donuts is $1.25 per pack and the price of a tea is $2.50. Ellie has $m to spend on these two goods each week. Pay careful attention to the instructions. Answers on paper and in myls sheet must match. a) (6 marks) On your paper: (i) write out the Lagrangian for this problem and derive the 3 first order conditions for solving Ellie's utility maximization problem; (ii) solve for Ellie's demand functions for donuts (D) and tea (T). b) (3 marks) Suppose Ellie's income is $22.50. On your paper solve for Ellie's optimal quantities of donuts and tea. Sketch Ellie's budget line (D is the x axis good). Label your graph and indicate the slope of the budget line. Record this optimal bundle in the myls answer box. c) (3 marks) Is tea a normal or inferior good? In the myls answer box, briefly explain your answer in words. Show graphical or mathematical support for your answer on your paper