Question

2) A drug lord wishes to optimize the area in which he will grow his coca plants. The area concerned has a river on one side and must be closed in with fencing on the other three sides. He has 500ft of fencing. Determine the dimensions of the field that will maximize the area. Show that this is indeed a maximum.

Answer 1

we assume that the area under consideration is a rectangle. Let be he dimensions. Since and area is , our problem is

Now, we have

Since square of a real number is always non-negative, is maximum when which gives . From we get .

Thus, the maximizing dimensions are and .

Since the problem

is equivalent to maximizing

and this is indeed maximum at , the proof is complete.