A rancher wishes to enclose a rectangular pasture with 320 feet of fencing. the fencing will be used on three sides of the pasture, and the fourth side of the pasture will be bounded by a wall. what dimensions should the pasture have in order to maximize its area?

Question

Marcel Navarro

Mathematics

2 March, 03:57

A rancher wishes to enclose a rectangular pasture with 320 feet of fencing. the fencing will be used on three sides of the pasture, and the fourth side of the pasture will be bounded by a wall. what dimensions should the pasture have in order to maximize its area?

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Answers (1)

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Kaiser · Answer 1

Let each side perpendicular to the wall be x

The parallel to the wall will be 320-2x

the area will be:

A (x) = x (320-2x)

A (x) = 320x-2x^2

This is a quadratic with a = - 2 and b=320

Maximum area will occur where x=-b/2a

=-320 / (-2*2)

=80 ft

thus the width will be 80 ft and the length will be:

length=320-2*80=160 ft