Next, let’s suppose a rancher wants to fence off a rectangular shaped enclosure that has two...

Next, let’s suppose a rancher wants to fence off a rectangular shaped enclosure that has two identical sections. You can think of this as a rectangle with an additional fence dividing the rectangle in half. For the sake of this question, he wants that additional fence running North-South (up-down). He still has 2400 feet of fencing that he can use. What are the dimensions that gives the enclosure the most area?

(a) Use the sketch of the pen below for this question. Appropriately label the relevant information in the sketch. Remember, East-West is right-left, North-South is up-down.

(b) Based on the sketch above, what equation is being maximized?

(c) Based on the sketch above, what equation represents the given constraint?

(d) Find the dimensions of the enclosure that gives the largest area.

(e) How much fence is used on the East-West sides? How much fence is used on the North-South sides? What is the ration of the amount of fence used on the East-West sides to the amount of fence used on the North-South sides?

Expert Solution

milcah answered 2 years ago

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