Please answer the following question with full explanations:

[10] Robinson Crusoe can produce two goods, X and Y, using the following production technologies: X = 7 Lx and Y = 3Ly . His preferences over the two goods can be expressed by his utility function U(X, Y) = XYZ and he is only willing to work a total of 6 hours in a day. a. [4] Derive the equation of his production possibilities frontier (express the quantity of good Y as a function of good X). b. [4] Solve for his utility maximizing consumption bundle. c. [2] What is the implicit price ratio that he faces? (Hint: Find the price ratio that is equal to his MRS)