Minimize $c=x+2 y$ subject to \[ \begin{array}{c} x+4 y \geq 18 \\ 7 x+y \geq 18 \\ x \geq 0, y \geq 0 \\ c=\square \\ (x, y)=(\square \end{array} \]

Step 1 ：This is a linear programming problem. We are asked to minimize the objective function \(c=x+2y\) subject to the constraints \(x+4y \geq 18\), \(7x+y \geq 18\), and \(x \geq 0, y \geq 0\).

Step 2 ：We can solve this problem using a method for linear programming.

Step 3 ：The optimal value of the objective function is 10.0, and the values of x and y that achieve this minimum are 2.0 and 4.0, respectively.

Step 4 ：Final Answer: \(c=\boxed{10}\), \((x, y)=(\boxed{2}, \boxed{4})\)