Problem
Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. HINT [See Example 1.] (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.) Maximize $p=2 x+3 y$ subject to $0.2 x+1.3 y \geq 3$ $6 x+\quad y \geq 17$ $x \geq 0, y \geq 0$. $p=$ $(x, y)=(\square)$
Solution
Step 1 ：Define the objective function as \(p=2x+3y\).
Step 2 ：Define the constraints as \(0.2x+1.3y \geq 3\), \(6x+y \geq 17\), and \(x \geq 0, y \geq 0\).
Step 3 ：Solve the linear programming problem using the defined objective function and constraints.
Step 4 ：Check the status of the solution. If the status is 0, the solution is optimal. If the status is 1, the feasible region is empty. If the status is 3, the objective function is unbounded.
Step 5 ：The result of the solution indicates that the problem is unbounded. This means that the objective function can take on arbitrarily large positive values.
Step 6 ：Therefore, there is no optimal solution to this problem.
Step 7 ：The final answer is that the function is \(\boxed{\text{UNBOUNDED}}\).
