Question

Warren wants to build a rectangular enclosure for his animals. one side of the pen will be against the barn, so he needs no fence on that side. the other three sides will be enclosed with wire fencing. if warren has 500 feet of fencing, you can find the dimensions that maximize the area of the enclosure.

a.let w be the width of the enclosure (perpendicular to the barn) and let l be the length of the enclosure (parallel to the barn). write an function for the area a of the enclosure in terms of w . (hint first write two equations with w and l and
a. solve for l in one equation and substitute for l in the other). a ( w ) = 1/2w
b.what width w would maximize the area? w = ft
c.what is the maximum area? a = square feet

Answer 1

l +2w = 500
a = lw

a) l = 500 -2w
.. a = (500 -2w)*w


b) The zeros of the above equation are w=0, w=250. The vertex of this quadratic is on the line of symmetry, halftway between the zeros, at w=125 ft.


c) a = (500 -2*125)*125 = 31,250 . . . . square feet