The owner of a motel has 5000 m of fencing and wants to enclose a rectangular plot of land that borders a straight highway. if she does not fence the side along the highway, what is the largest area that can be enclosed?

The perimeter in this case is:
 y + 2x = 5000
 The area is:
 A = x * y
 We rewrite the area:
 A = x * (5000-2x)
 A = 5000x-2x ^ 2
 We derive:
 A '= 5000-4x
 We equal zero and clear x:
 0 = 5000-4x
 4x = 5000
 x = 5000/4
 x = 1250
 We look for the other dimension:
 y = 5000-2x
 y = 5000-2 (1250)
 y = 5000-2500
 y = 2500
 Then, the area will be:
 A = (2500) * (1250)
 A = 3125000 m ^ 2
 
 The largest area that can be enclosed is:
 A = 3125000 m ^ 2

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