Calculus

A rancher wants to construct two identical rectangular corrals using 300 ft of fencing. The rancher decides to build them adjacent to each other, so they share fencing on one side. What dimensions should the rancher use to construct each corral so that together, they will enclose the largest possible area?

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  1. easy way. Let the length be 2x and the width be y.
    Then 2x=3y=150 maximizes the area
    The corral will be 150 by 50 (two 75x50 corrals)

    Or, do the math
    2x+3y = 300
    y = 100 - 2x/3
    area a = 2xy = 2x(100 - 2x/3) = 200x - 4/3 x^2
    Max area at the vertex of that parabola. Use algebra or calculus.

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