Suppose that a homeowner has 380 feet of fencing and she would would like to enc

Question

Suppose that a homeowner has 380 feet of fencing and she would would like to enclose a rectangular area at the back of her house with no fencing needed along the back of the house (this means that only 3 sides of fencing are needed as the house itself will serve as the fourth side). What is the maximum area that she can enclose with the fencing that she has available?

Explanation / Answer

A= lb now 380 = 2b + l l= 380-2b so A= 380b - 2b^2 to maximize A we differentiate it with respect to b and equate it to 0 to find the critical points => 380 -4b = 0 b = 95 (double differentiation is negative confirming that it is local maxima) l = 190 maximum area that can be covered is 18050

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