Has available 480480 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?

Question

Donald Mayer

Mathematics

11 October, 11:46

Has available 480480 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?

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Winston Santana · Answer 1

I assume you meant 480 yards and not 480480 yards.

a) 2L + 2W = 480 so 2L = 480 - 2W; L = 240 - W; The area of the rectangle (A) is LW; A = LW; A = (240 - W) W; A = 240W - W^2; F (W) = 240W - W^2.

b) The maximum area of the rectangle is when the derivative of F (W) = 0. F' (W) = 240 - 2W; 0 = 240 - 2W; W = 120. The area of the rectangle is greatest when W = 120.

c) The maximum area is A = (120) (120) = 14400 ft^2