SOLUTION: A rectangular field is to be subdivided in 6 equal fields. There is 1200 feet of fencing available. Find the dimensions of the field that maximizes the total area. (List the longer

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Question 409607: A rectangular field is to be subdivided in 6 equal fields. There is 1200 feet of fencing available. Find the dimensions of the field that maximizes the total area. (List the longer side first)
Answer by solver91311(24713) About Me  (Show Source):
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There are 2 long sides and then 7 pieces of fence that equal the short side measure. Draw yourself a picture to check my numbers.

Hence the 1200 feet of fencing must be used in the following way:



Solving for we get:



Since

By substitution we get:



Since the Area function is continous and twice differentiable over its domain, take the first derivative:



set it equal to zero



Then solve for the value of the independent variable that gives an extreme point:



Take the second derivative:

therefore is a maximum.

Substitute back into and solve for to get the long dimension.

John

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