The utility function for an individual is given by the equation: U = X1 0.25X2 0.75 and their budget constraint is P1X1 + P2X2 =M (i) Using the Lagrange, and showing all work, Derive the demand functions for good X1 and good X2 (ii) Given that the price for good 1, p1= k2.5 and the price for good 2, p2=k5, and the consumer’s income is k100. Calculate and graphically present the optimal choice for good 1 and good 2

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