Question: Consider the nonlinear optimization model stated below. [ begin{array}{ll} text { Min } & 2 X^{2}-18 X+2 X Y+Y^{2}-12 Y+52 text { s.t. }

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Consider the nonlinear optimization model stated below. \[ \begin{array}{ll} \text { Min } & 2 X^{2}-18 X+2 X Y+Y^{2}-12 Y+52 \\ \text { s.t. } & X+4 Y \leq 7 \end{array} \] (a) Find the minimum solut $Min } & 2 X^{2}-18 X+2 X Y+Y^{2}-12 Y+52 \\ \text {$

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