Question: Find the minimum value of \(F\left( x,y \right)=5x+7y\) subject to

\[\begin{aligned} & 2x+3y\ge 6 \\ & 3x-y\le 15 \\ & -x+y\le 4 \\ & 2x+5y\le 27 \\ & x,y\ge 0 \\ \end{aligned}\]