BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 3.1, Problem 71E
To determine

To find: The dimensions of the field of largest area that a farmer can fence.

Expert Solution

Answer to Problem 71E

The dimensions of the field of largest area that the farmer can fence is 600ft by 1200ft .

Explanation of Solution

Given information:

A farmer has 2400ft of fencing and wants to fence off a rectangular field that borders a straight river. The farmer doesn’t fence along the river.

Calculation:

As per given, assume that the length of the rectangular field is equal to xft .

As the length is fenced two times i.e. length of the fence for these two sides is equal to 2xft and as the total fence is 2400ft . So, the breadth of the rectangular field is equal to 24002xft .

Use the formula for the area of the rectangular region.

  A=L×BA=x×(24002x)A=2400x2x2

So, the area function of the rectangular region is given by g(x)=2400xx2 . To maximize the area of the rectangular region graph the area function g(x)=2400xx2 .

To graph a function y=2400x2x2 , follow the steps using graphing calculator.

First press “ON” button on graphical calculator, press Y= key and enter right hand side of the equation y=2400x2x2 after the symbol Y1 . Enter the keystrokes 2400X2X^2 .

The display will show the equation,

  Y1=2400X2X^2

Now, press the GRAPH key and TRACE key to produce the graph of given function in standard window as shown in Figure (1).

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 3.1, Problem 71E

Figure (1)

As observed from the graph, the area function has maximum value at x=600 .

So, the length of the rectangular region is equal to 600ft and the breadth of the rectangular region is equal to 24002(600)=1200ft .

Therefore, the dimensions of the field of largest area that the farmer can fence is 600ft by 1200ft .

Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!