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

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Basic Math

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

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

(d) Find the dimensions of the enclosure that gives the largestarea.

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

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