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 Consider the problem of maximizing the utility function u(x, y) = x'/2 + y'/2 on the budget set {(x, y) e R px + y = 1}

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 Consider the problem of maximizing the utility function u(x, y) = x'/2 + y'/2 on the budget set {(x, y) e R px + y = 1}. Show that if the nonnegativity constraints x > 0 and y > 0 are ignored, and the problem is written as an equality-constrained one, the resulting Lagrangean has a unique critical point. Does this critical point identify a solution to the problem? Why or why not?