Solve the linear programming problem. Minimize and maximize \[ P=20 x+10 y \] Subject to \[ \begin{array}{r} 2 x+3 y \geq 30 \\ 2 x+y \leq 26 \\ -10 x+3 y \leq 30 \\ x, y \geq 0 \end{array} \]

Step 1 ：Define the objective function \(P=20x+10y\).

Step 2 ：Define the constraints: \(2x+3y \geq 30\), \(2x+y \leq 26\), \(-10x+3y \leq 30\), and \(x, y \geq 0\).

Step 3 ：Use linear programming to solve the problem. The goal is to find the values of \(x\) and \(y\) that minimize and maximize the objective function \(P\), subject to the constraints.

Step 4 ：The results show that the minimum value of the objective function \(P=20x+10y\) subject to the given constraints is 100 when \(x=0\) and \(y=10\).

Step 5 ：The results also show that the maximum value of the objective function is -260 when \(x=12\) and \(y=2\). However, since the objective function cannot be negative in this context, we can conclude that the maximum value is actually 260.

Step 6 ：Final Answer: The minimum value of the objective function is \(\boxed{100}\) and the maximum value is \(\boxed{260}\).