Solve the following linear programming problem. Restrict $x \geq 0$ and $y \geq 0$.
\[
\begin{array}{c}
\text { Maximize } f=3 x+4 y \text { subject to } \\
\begin{array}{r}
x+y \leq 11 \\
2 x+y \leq 16 \\
y \leq 8
\end{array} \\
(x, y)=( \\
f=\square
\end{array}
\]
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Step 1 ：The problem is a linear programming problem. The goal is to maximize the function \(f=3x+4y\) under the constraints \(x+y \leq 11\), \(2x+y \leq 16\), and \(y \leq 8\). We also have the restrictions \(x \geq 0\) and \(y \geq 0\).

Step 2 ：To solve this problem, we need to convert the maximization problem to a minimization problem by multiplying the objective function by -1.

Step 3 ：Then, we can use the linprog function from scipy.optimize to solve the problem.

Step 4 ：The output from the Python code shows that the optimal solution is \(x=3\) and \(y=8\). The optimal value of the objective function is \(f=-(-41)=41\).

Step 5 ：This means that the maximum value of \(f=3x+4y\) under the given constraints is 41, achieved at \((x, y) = (3, 8)\).

Step 6 ：Final Answer: \((x, y) = \boxed{(3, 8)}\), \(f = \boxed{41}\).