1. Robinson Crusoe can produce two goods, X and Y, using the following production technologies:
? = 5√?? and ? = 6??
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.  Derive the equation of his production possibilities frontier (express the quantity of good Y as a function of good X).
b.  Solve for his utility maximizing consumption bundle.
c.  What is the implicit price ratio that he faces? (Hint: Find the price ratio that is equal to his MRS)
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