09 - 11 Rectangular Lot Problems in Maxima and Minima

Problem 9
What should be the shape of a rectangular field of a given area, if it is to be enclosed by the least amount of fencing?

Solution 9

 

Problem 10
A rectangular field of given area is to be fenced off along the bank of a river. If no fence is needed along the river, what is the shape of the rectangle requiring the least amount of fencing?

Solution 10

 

Problem 11
A rectangular lot is to be fenced off along a highway. If the fence on the highway costs m dollars per yard, on the other sides n dollars per yard, find the area of the largest lot that can be fenced off for k dollars.

Solution 11

 
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