A farmer decides to build a fence to enclose a rectangular field in which he wil

Question

A farmer decides to build a fence to enclose a rectangular field in which he will plant a crop. He has 1200 feet of fence to use and his goal is to maximize the area of his field. a. What is the width of the field if the length of the field is 300 feet? Preview b. What is the width of the field if the length of the field is 208.16 feet? *Preview c. Define a function k that determines the length of the fence in feet in terms of the fence's width in feet, w, given the total amount of fence is 1200 feet. Preview d. Which of the following represents the area of the rectangular field in terms of the fence's width in feet, w? wk() Ow k() ONone of the above e. Define a function f that expresses the area of the field (measured in square feet) as a function of the width of the side of the field w (measured in feet). Preview f. Use your graphing calculator to graph the function you defined in part (e). Based on your graph, what is the maximum area of the enclosed field? Preview

Explanation / Answer

2l+2w=1200

l+w=600

a. l=300

w=600-300=300 feet

b. w=208.16 feet

l=600-208.16=391.84 feet

c .k(w)=600-w

d. Area= length *width = k(w)*w

Correct option is the third option

e.A=w(600-w) =600w -w2

f. Maximum area= 300*300 =90000 square feet

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