aNSWER PLEASSE

Question 25 (12 points) Elle'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 myis sheet must match. al (6 marks) On your paper. write out the Lagrangian for this problem and derive the 3 first order conditions for solving Ellie's utility maximization problem; () solve for Ellie's demand functions for donuts (D) and tea (T). b) (3 marks) Suppose Ellie's income is $30. On your paper solve for Ellie's optimal 12 quantities of donuts and tea. On your paper sketch Ellie's budget line (D is the x axis iv good. Label your graph and indicate the slope of the budget line. Record this optimal bundle in the myis answer box. c) (3 marks) Is tea a normal or inferior good? In the myls answer box, briefly explain 15 your paper. Your answer in words. Provide mathematical or graphical support for your answer on MacBook At