Find the maximum value and the minimum value of the function and the values of $x$ and $y$ for which they occur. \[ P=20 x-4 y+64, \text { subject to } 7 x+9 y \leq 63,0 \leq y \leq 4 \text {, and } 0 \leq x \leq 5 \text {. } \] The maximum value of the function is and it occurs where $x=$ and $y=$ The minimum value of the function is and it occurs where $x=$ and $y=$ (Do not round until the final answer. Then round to two decimal places as needed.)

Step 1 ：Define the function to be maximized or minimized as \(P=20x-4y+64\).

Step 2 ：Define the constraints as \(7x+9y \leq 63\), \(0 \leq y \leq 4\), and \(0 \leq x \leq 5\).

Step 3 ：Find the vertices of the feasible region defined by the constraints.

Step 4 ：Substitute the coordinates of the vertices into the function \(P\).

Step 5 ：Compare the function values to find the maximum and minimum values and the corresponding values of \(x\) and \(y\).

Step 6 ：The maximum value of the function is \(100\) and it occurs where \(x=5\) and \(y=0\).

Step 7 ：The minimum value of the function is \(16\) and it occurs where \(x=0\) and \(y=4\).

Step 8 ：\(\boxed{\text{Final Answer: The maximum value of the function is } 100 \text{ and it occurs where } x=5 \text{ and } y=0. \text{ The minimum value of the function is } 16 \text{ and it occurs where } x=0 \text{ and } y=4.}\)