Lew Hodgett wrote:
Bill wrote:
A farmer has 20 feet of fencing and wishing to build a rectangular
pen against his barn (by adding 3 sides), maximizing the area. What
should the dimensions be? Note: It makes the kids smile if I
include a little animal in the diagram.
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Not enough information to develop 3 independent equations.

You can use Taylor's theorem of approximation to determine
that a 5 ft x 10 ft pen with the 10 ft side parallel to barn wall will
yield max area.
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W = Width
L = Length
A = Area

2W + L = 20

A = WL
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WHEN W = 7, THEN L = 6
A = 42

WHEN W = 6, THEN L = 8
A = 48

WHEN W = 5, THEN L = 10
A = 50

WHEN W = 4, THEN L = 12
A = 48

WHEN W = 3, THEN L = 14
A = 42

Ye gads you are making me dig.

Haven't used most of this stuff in over 50 years.

Lew



Instead of using 2 variables L and W, try it with just 1 (say just L or
W), you can write the area as a single equation/function of it. You'll
have a quadratic equation whose graph is a parabola... This will lead
you not only an answer, but the fact that the answer lies at the vertex
of a parabola opening downwards will justify for you that it is the
unique best answer.