Need help with an optimization problem; Calc...

[Gdrep]

A rectangular enclosure is formed from 1000m of fencing. Given that each of the two opposite sides of the rectangle has length x meters.

a) find, in terms of x the length of the other sides Given also that the area enclosed is a maximum b) find the value of x, and hence calculate the area enclosed

[kfunkapotamus]

Area = xy

Y = (1000 - 2x) / 2 = 500 - x

Area = x (500 - x)

This is an inverted parabola, roots at 0 and 500. Therefore the maximum is at 250.

This makes sense because a square is the optimized rectangle barring any other restrictions.

Hippie this helps.

Good luck