u(x, y) = x +y. a)Prove the ratio amount of good x to y is py/px. (Tangency

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u(x, y) = x +y. a)Prove the ratio amount of good x to y is py/px. (Tangency condition) b) Consider the preferences represented by u(x, y) = max {x, y}.Illustrate some representitive indifference curves. c) Now consider the preferences represented by u(x, y) = xy. Illustrate some representative indifference curves.