3. [10] A representative agent (RA) can produce two goods, xylophones [denoted X) and yogurt (denoted Y], using the following production technologies: X = 31/1,); and Y = 41.}.- where L denotes labour input measured in hours. The agent's preferences over the two goods can be expressed by their utility function U(X, Y) = XYZ and they are only willing to work a total of 8 hours in a day. a. [4] Derive the equation of the RA's production possibilities frontier (express the quantity of good Y as a function of good X). b. [4] Solve for the agent's utility maximizing consumption bundle. c. [2] What is the implicit price ratio faced by the RA? (Hint: Find the price ratio that is eqaai to his MR5)