OPTIMIZATION PROBLEM 1

Helen buys 2 goods: clothing (x) and food (y). One unit of clothing costs $15, while one unit of food costs $5. Helen has a budget of $100.

1. Suppose her preferences are represented by the utility function U (x, y) =lnxy. Using opti-mization techniques, determine Helen's optimal bundle and illustrate graphically

2. Suppose her preferences are represented by the utility function U (x, y) = 10lnx + y. Determine Helen's optimal bundle and illustrate graphically

3. Suppose her preferences are represented by the utility function U (x, y) = 10lnx + y, but now the price of food increases to $15, while the price of clothing remains at $15. Determine Helen's optimal bundle and illustrate graphically

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