A farmer has 3000 feet of fencing to use on a new enclosure. The new enclosure will go up against existing fencing so one side does not need additional fencing. If the farmer wants to subdivide the enclosure to have 3 pens, what is the maximum total area the farmer can enclose?

375000 ft^2

Step-by-step explanation:

From the statement that we have that it would be 1 time the length and 2 times the width because one side is not necessary and also we must take into account that it would be divided by 3 equal enclosures therefore we will use 1000 feet (3000/3) so Therefore, the perimeter would be equal to:

1000 = l + 2 * w

we solve for w:

l = 1000 - 2 * w

Also the area is equal to:

A = w * l

replacing:

A = w * (1000 - 2 * w)

A = 1000 * w - 2 * w ^ 2

We derive:

A ' = 1000 - 4 * w

Let's equal 0:

1000 - 4 * w = 0

w = 1000/4

w = 250

replacing and we calculate l:

l = 1000 - 2 * 250

l = 500

A = 250 * 500

A = 15,000 ft ^ 2

Which means that for each subdivision the maximum area would be 125000 square feet and the total would be:

125000 * 3 = 375000 ft ^ 2