A farmer decides to build a fence to enclose a rectangular f

A farmer decides to build a fence to enclose a rectangular field in which he will lard a crop. He has 900 feet of fence to use and his goal is so maximize the area of his field. a. What is the width of the field if the length of the field is 200 feet? b. What is the width of the field if the length of the field is 306, 41 feet? 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 900 feet. d. Which of the following represents the area of the rectangular field in terms of the fence\'s width in feet, w? omega middot I omega^2 omega + k(omega) w middot k(omega) None 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 omega (measured in feet). f. Use your graphing calculate to graph the function you defined in part (c). Based on your graph, what is the maximum area of the enclosed field?

Solution

a) perimeter of field = length of fence = 900 ft

2*length + 2*width = 900

width = 450 -200 = 250 ft

b) if lenght = 304.61 ft

width = 450 - 304.61 = 145.39 ft

c) width = w ; k = length

2w +2k = 900 ; w +k = 450

k = 450 - w;

k(w) = 450 - w

d) Area = w*k(w)

e) Area = length*width = (450 -w)w

f(w) = ( 450 -w)w = -w^2 +450w