Question: Find the maximum value of the function [F=x_{1} x_{2}] subject to the constraints [begin{aligned}& x_{1}^{2}+x_{2}^{2} leq 4 & x_{1}, x_{2} geq 0 text { and

Find the maximum value of the function

\[F=x_{1} x_{2}\]

subject to the constraints

\[\begin{aligned}& x_{1}^{2}+x_{2}^{2} \leq 4 \\& x_{1}, x_{2} \geq 0 \text { and integer }\end{aligned}\]

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