The point which provides the solution of the linear programming problem, maximize subject to constraints , and is
Explanation for the correct option:
Step 1: Find the critical points graphically
In the question, Four inequalities , and is given.
Draw the graph of the given inequalities.
From the graph, it is clear that the critical points are and .
Step 2: Find the maximum value of the given function
A function is given in the question.
Compute the values of the given function at critical points as follows:
For .
So, the value of the given function is at .
For .
So, the value of the given function is at .
For .
So, the value of the given function is at .
For .
So, the value of the given function is at .
Since the maximum value of the given function is at .
Therefore, The given function maximizes at .
Hence, option is the correct answer.