Find the maximum value of the function $z=4 x+10 y$ subject to the following cons \[ \left\{\begin{array}{c} x \geq 2 \\ y \geq 2 \\ 6 x+7 y \leq 68 \end{array}\right. \]

Step 1 ：Define the objective function as \(z=4x+10y\).

Step 2 ：Set the constraints as \(x \geq 2\), \(y \geq 2\), and \(6x+7y \leq 68\).

Step 3 ：Use a linear programming solver to find the maximum value of the objective function subject to the constraints.

Step 4 ：The solver returns the optimal value of the function and the values of the variables that give the optimal value.

Step 5 ：The maximum value of the function is 88 when \(x=2\) and \(y=8\).

Step 6 ：Final Answer: The maximum value of the function \(z=4x+10y\) subject to the given constraints is \(\boxed{88}\) when \(x=\boxed{2}\) and \(y=\boxed{8}\).