Question

A Aav > AL I A. Av. Av Dictate Styles Styles Pane 1. A rancher has 300 feet of fencing to enclose two adjacent rectangular pieces of land. --- 1 -> -- W a. Write an equation that relates length and width to the total given distance. [2 points] 1 + W = b. Use your equation in a. to write the total area (A) as a function of only one of these variables. [3 points) c. Find the dimensions that will yield a maximum area. [3 points] d. What is the maximum area? [2 points) e. Which of the following is true about your answer in 1d? [1 point] (A) This is an absolute maximum. (B) This is a relative maximum that is not absolute. (C) Neither (A) nor (B) glish (United States) Focus 29 C

Answer 1

(1) Given: Jotal length = Gooft.. l Ko W w l Total length from figure lalt wtW+W it should be equal to 300 7 gl + 3 w = 300 2 le+ 3 WE 3oole ANS Area= length x width A = low D from past (a) ZW= 300 al 300-21).( Put w value in o) 3 As ex 1/43 300-21) As (300 l - 912) ANS 5

(c) Differentiate above function with respect to 'l' to Sind maximum area. da dl die (3000-203) (Take constant outside) 300 de 2d642 ) de de ( 300-2.21) (do (3cm) = hach-2 da dl 5 (300 - 41) Equate it equal to zero. 3 (300 - 4l)=0 -> 4 ln Zoo la Zoo 4 45 fout (30o-al) 3 5 ( 300-2445) ( 306-150) 1 3 50 foot

Dimensions: l= 75 ft W = Soft } ANS (d) Area = exw Put = 75, W = so to find maximum area Amax 75 x 50 2 - 3750f42 2 maximum area a 3750 ff 2 ANS ce Sign analysis: dA dl. ou le 150 the ve 15 150 increasing decreasing Crives absolu.Le maximum area А This is an absolute maximum ANS