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Consider an individual who has a utility function U(X, Y) = 2X(1/2) + y(1/2) the prices of goods X and Y are given by pX = $8 and pY = $2, and the income level of consumer is I = $80. 3-a) Write the consumer's utility maximization problem (formally, as we wrote in the lectures). 3-b) Write the Lagrangian function associated to the maximization problem. 3-c) Write the first order conditions (FOC). 3-d) Find the consumption bundle that maximizes consumer's utility