Posted by T.Gracken on November 07, 2002 at 10:43:04:
In Reply to: word problem posted by mj on November 06, 2002 at 23:45:57:
: A rectangular garden 200 square feet in area is to be fenced off against rabbits. Find the dimensions that will require the least amount of fencing if one side of the garden is already by a barn.
suppose W is the width of the garden and L is the length of the garden.
then area = LW = 200
amount of fence needed is 2W + L (the two widths and one length, since the other length is the side of the barn)
let F = amount of fence (linear feet)
then F = 2W+L and L=200/W (from above)
so minimize F for F=2W + 200/W
(i.e. take derivative, determine critical values in domain, test, etc.)