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Prove that the utility function u(x, y) = In(x + y) + 7(x^2+ 2xy + y^2) + 43 represents preferences over perfect substitutes. Prove this in two ways (parts a and b): (a) Show that u(x,y) is an increasing transformation of a perfect substitutes utility function. (b) Show that the indifference curves are straight lines (i.e. show that the MRS is constant and equal to -1)