Can someone help with this **Problem Statement:**You have 830 ft of fencing to make a pen for hogs. You have a river on one side of your property and will use the river as one side of the pen. You want to maximize the area of the pen using all of the available fencing. Use the picture below for this problem.**Diagram Description:**The diagram shows a rectangular pen adjacent to a river. The river acts as one side of the rectangle. The rectangle has a length denoted as \( l \) and a width denoted as \( w \).**Mathematical Details:**- The area of the pen as a function of its length, \( l \), is: \[ A(l) = \ \_\_\_ \ \text{ft}^2 \]- For what value of \( l \) will \( A'(l) = 0 \)? \[ l = \ \_\_\_ \ \text{ft} \]- The area of the pen as a function of its width, \( w \), is: \[ A(w) = \ \_\_\_ \ \text{ft}^2 \]- For what value of \( w \) will \( A'(w) = 0 \)? \[ w = \ \_\_\_ \ \text{ft} \]- The maximum area of the pen is \(\_\_\_ \text{ft}^2\)

Given Length of the field is l Given width of the fiels is w Total perimeter of the field is given…

You have 830 ft of fencing to make a pen for hogs. You have a river on one side of your property and will use the river as one side of the pen. You want to maximize the area of the pen using all of the available fencing. Use the picture below for this problem. 1 W The area of the pen as a function of its length, 1, is: A(1) ft² = For what value of I will A'(1) = 0? 1 ft The area of the pen as a function of its width, w, is: A(w) = ft² For what value of w will A'(w) = 0? W = ft The maximum area of the pen is ft²

You have 830 ft of fencing to make a pen for hogs. You have a river on one side of your property and will use the river as one side of the pen. You want to maximize the area of the pen using all of the available fencing. Use the picture below for this problem. 1 W The area of the pen as a function of its length, 1, is: A(1) ft² = For what value of I will A'(1) = 0? 1 ft The area of the pen as a function of its width, w, is: A(w) = ft² For what value of w will A'(w) = 0? W = ft The maximum area of the pen is ft²

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Can someone help with this

**Problem Statement:**

You have 830 ft of fencing to make a pen for hogs. You have a river on one side of your property and will use the river as one side of the pen. You want to maximize the area of the pen using all of the available fencing. Use the picture below for this problem.

**Diagram Description:**

The diagram shows a rectangular pen adjacent to a river. The river acts as one side of the rectangle. The rectangle has a length denoted as \( l \) and a width denoted as \( w \).

**Mathematical Details:**

- The area of the pen as a function of its length, \( l \), is:
\[
A(l) = \ \_\_\_ \ \text{ft}^2
\]

- For what value of \( l \) will \( A'(l) = 0 \)?
\[
l = \ \_\_\_ \ \text{ft}
\]

- The area of the pen as a function of its width, \( w \), is:
\[
A(w) = \ \_\_\_ \ \text{ft}^2
\]

- For what value of \( w \) will \( A'(w) = 0 \)?
\[
w = \ \_\_\_ \ \text{ft}
\]

- The maximum area of the pen is \(\_\_\_ \text{ft}^2\)

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