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Question

A farmer wants to enclose two separate but adjacent pastures next to the river which runs along one edge of his farm: one for cows and one for sheep. He will not use fencing along the river. He has 120 m of fencing to use. What is the maximum area he can enclose?

Answer 1

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| | |

| | | W

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L

A = LW. ; L + 3W = 120. so L = 120 - 3W

A = (120 - 3W)(W) = -3W² + 120W

This area function is quadratic in W, meaning it will graph as a concave down parabola with a vertex at W = -b/2a = 20. L = 120 - 3(20) = 60

The ideal dimensions are 20 x 60 m , which will enclose the maximum area of 1,200 m².