Solve the linear programming problem.
Minimize and maximize
\[
z=50 x+10 y
\]
Subject to
\[
\begin{aligned}
2 x+y & \geq 72 \\
x+y & \geq 48 \\
x+2 y & \geq 60 \\
x, y & \geq 0
\end{aligned}
\]

Step 1 ：Define the objective function as \(z = 50x + 10y\).

Step 2 ：Set the constraints as follows: \(2x + y \geq 72\), \(x + y \geq 48\), \(x + 2y \geq 60\), and \(x, y \geq 0\).

Step 3 ：Convert the constraints into a form that can be understood by the linear programming solver. The constraints are given in the form \(Ax \geq b\), where \(A\) is a 2D array containing the coefficients of the inequalities, and \(b\) is a 1D array containing the right-hand side of the inequalities.

Step 4 ：Specify the bounds for the variables \(x\) and \(y\). In this case, both \(x\) and \(y\) are greater than or equal to 0.

Step 5 ：Attempt to solve the problem using a linear programming solver.

Step 6 ：The result indicates that the problem is unbounded, which means that there is no finite optimal solution. This can happen when the feasible region (the region that satisfies all constraints) is not bounded, i.e., it extends to infinity in some direction.

Step 7 ：In this case, it means that we can increase the value of the objective function \(z = 50x + 10y\) indefinitely without violating any of the constraints, so there is no maximum value.

Step 8 ：Similarly, we can decrease the value of the objective function indefinitely without violating any of the constraints, so there is no minimum value either.

Step 9 ：\(\boxed{\text{Final Answer: The problem is unbounded and does not have a finite optimal solution.}}\)