3. Assume that Adam's utility from consuming good X and good Y is given by the following function: U = 4X 0.8Y 0.2 Where X is the quantity of good X while Y is the quantity of good Y. Assume the price of X (PX) is 45, the price of Y (PY) is 15, and he has a budget of 2250 to spend on the two goods.

a. Using the Lagrange multiplier, calculate Adam's optimal consumption bundle (You must clearly show all working and explain the economic intuition to receive the marks for this question).

b. Calculate Adam's utility at his optimal consumption bundle (You must clearly show all working and explain the economic intuition to receive the marks for this question).

c. Calculate at Adam's optimal consumption bundle and provide an economic interpretation of its value (You must clearly show all working and explain the economic intuition to receive the marks for this question).

d. Illustrate your answers to all the previous parts to this question on a clearly drawn and labelled indifference curve diagram. In particular, illustrate and explain: - The intercepts and slope of the budget constraint - The optimum consumption combination. - The optimal quantity of both goods. - The level of utility at the optimum consumption bundle