O 3.3/4 points | Previous Answers SPreCalc7 3.1.059. My Notes O Ask Your Teac A

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O 3.3/4 points | Previous Answers SPreCalc7 3.1.059. My Notes O Ask Your Teac A farmer has 2400 ft of fencing and wants to fence off a rectangular field that borders a straight river. He does not need a fence along the river (see figure). What are the dimensions of the field of largest area that he can fence? the (a) Experiment with the problem by drawing several diagrams illustrating the situation. Calculate the area of each configuration, and use your results to estimate the dimensions of the largest possible field. (Enter your answers as a comma-separated list.) (b) Find a function that models the area of the field in terms of one of its sides. A(x) = 1-2x" + 2400x (c) Use your model to solve the problem, and compare with your answer to part (a). Maximum area occurs at the following values. smaller dimension 600 larger dimension1200 ft ft Need Help? Read it Watch It Submit Answer Save Progress

Explanation / Answer

Let x be the width and y be the length of rectangular fence .

Perimeter of fence = 2400 ft

2x+y=2400

y=2400-2x--------1)

Area of rectangle =A= X.y

A=x (2400-2x)

A=2400x-2x2 -----2)

Differentiate with respect to x

A'=2400-4x

For maxima A'=0

x=600 ft

Then y=1200 ft

Hence maximum area

A=x.y

=1200×600

=720000 sq.ft

Maximum area is 720000 sq .ft when x=600 ft and y=1200ft

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