Diana has available 80 yards of fencing and wishes to enclose a rectangular area. (a) Express the area A of the rectangle as a function of the width W of the rectangle. (b) For what value of W is the area largest? (c) What is the maximum area?
Accepted Solution
A:
Answer:a) A = 40*W – W^2b) W = 20c ) A = 400Step-by-step explanation:a) Let beW = width W of the rectangle
L = lenght of the rectangle
P = Perimeter of the rectangleA = area of the rectangle
P = 2*L + 2*W
80 = 2*L + 2*W
So, 2*L = 80 – 2*W
L = 40 – W
A = L * W
Replacing L
A = (40 – W)*W
A = 40*W – W^2
b) To find the máximum value for W, we derivate area and equal to zero
A’ = 40 – 2*W
40 – 2*W = 0
2*W = 40
W= 20
c) With the value for W, we find L
L = 40 – W
L = 40 – 20
L = 20
A = W*L
A = 20 * 20
A = 400