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4. A consumer lives on an island where she produces two goods, x and y according to production possibility frontier: x2+y2200, and she consumes all the goods herself. Her utility function is U=xy3. She also faces an environmental constraint on her production as x+y20. (a) Find her optimal x and y. (10 points) (b) Check whether the sufficient conditions are satisfied at the x and y you found. (5 points).

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4. A consumer lives on an island where she produces two goods, x and y according to production possibility frontier: x2+y2200, and she consumes all the goods herself. Her utility function is U=xy3. She also faces an environmental constraint on her production as x+y20. (a) Find her optimal x and y. (10 points) (b) Check whether the sufficient conditions are satisfied at the x and y you found. (5 points)

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