Maximizing Area

Question

A farmer has 200 ft of fencing and wants to build three adjacent rectangular corrals. Determine the dimensions that should be used to maximize the area, and find the area of each individual corral.

 

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x |        x |          x |           x |

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                      y

 

Answer 1

200 - 2y = 4x

100 - y = 2x        divide both sides by 2

100 = 2x + y       add y to both sides

100 - 2x = y        subtract 2x from both sides

 

A = x(100 - 2x)

A = 100x - 2x²

A = -2x² + 100x

 

Maximum is at x = -100/2(-2)       maximum at -b/2a

Maximum at x = 25

y = 50

 

What is the area of each pen?