David has available 400 yards of fencing and wishes to enclo

David has available 400 yards of fencing and wishes to enclose a rectangular area. (a) Express the area A of the rectangle as a function of the width Wof the rectangle (c) What is the maximum area? (b) The area is largest for W yards. (Simplify your answer.) (c) The maximum area is Square yards. (Simplify your answer) Enter your answer in each of the esc

Solution

a)
let the length be L and width be W
then perimeter = 400 ayrd
2*(L+W) = 400
L = 200 - W

A = L*W
= (200-W)*W
= 200W - W^2
A(W) = 200W - W^2
b)
To find teh largest area put , dA/dW = 0
dA/dW = 200-2w
200-2W = 0
gives W = 100
Answer: 100 yards
c)
Area max = 100*100 = 10000 square yards