Linear Programming Problem

Step 1: Understanding the constraints. The given constraints are: These constraints define a feasible region in the first quadrant where the values of and lie.

Step 2: Identifying the feasible region. The inequalities define a strip in the first quadrant between the lines: - (lower boundary). - (upper boundary). However, for a solution to exist, the feasible region should be a bounded region where an optimal solution can be determined.

Step 3: Checking feasibility for optimization. Since the given constraints do not form a closed bounded region (it extends infinitely), there is no minimum bound for the function . Thus, the solution region is not feasible for determining the minimum value.

Conclusion: Since the feasible region does not bound the function properly, the minimum value cannot be determined.

Step 1: The objective function is .

Step 2: To find the maximum value of the objective function, we evaluate at each of the given vertices: - At : - At : - At : - At :

Step 3: The maximum value of is 162, which occurs at the vertex . Thus, the maximum value of the objective function is .