3. [10] Robinson Crusoe can produce two goods, X and Y, using the following production technologies: = 7 and = 3 . His preferences over the two goods can be expressed by his utility function (, ) = 2 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)