The maximum value of in the following equation , where and for and is _________
Step 1: Find the critical points of the given function.
In the question, a function is given, and the constraints , , , and is also given.
Draw a graph describing the given inequalities as follows:
From the graph, it is clear that the critical points are and .
Step 2: Find the maximum value of the given function.
Since, the critical points are and .
Evaluate for as follows:
So, the value of for is .
Similarly, Evaluate for as follows:
So, the value of for is .
Similarly, Evaluate for as follows:
So, the value of for is .
Therefore, the maximum value of the given function is .
Hence, the answer is .