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Multivariable CalculusHardOptimization & Lagrange Multipliers

Optimization & Lagrange Multipliers · Hard problem

Find the minimum value of f(x,y)=x2+xy−12x+2y2−20y+69f(x, y) = x^{2} + x y - 12 x + 2 y^{2} - 20 y + 69.