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In: Math

Suppose a rancher wants to fence off a rectangular shaped enclosure. He has 2400 feet of...

Suppose a rancher wants to fence off a rectangular shaped enclosure. He has 2400 feet of fencing that he can use. What are the dimensions that gives the enclosure the most area?

(a) Draw a sketch of the pen in this question. Appropriately label the relevant information in your sketch.

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

(c) Based on your 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?

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