   Chapter 10.4, Problem 15E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Minimum fence Two equal rectangular lots are to be enclosed by fencing the perimeter of a rectangular lot and then putting a fence across its middle. If each lot is to contain 1200 square feet, what is the minimum amount of fence needed to enclose the lots (include the fence across the middle)?

To determine

To calculate: The minimum amount of fence required to enclose the lots.

Explanation

Given Information:

Two rectangular lots of 1200 sq.ft each are enclosed by fencing the perimeter of the rectangular lot (includes a fence across the middle).

Formula used:

To find the maximum value, calculate the relevant stationary value of an equation. Differentiate the function with respect to the independent variable and equate it to 0. the relevant value is the stationary value that satisfies the provided conditions.

If the second derivative of the provided function is less than zero, then substituting the value of the independent variable will give the maximum value of the equation.

The power rule is used for a function in which the expression can be written as every term raised to a power (be it fractional, positive or negative). For the function f(x)=xn, the derivative is

ddx[xn]=nxn1

Calculation:

As given, two rectangular lots of 1200 sq.ft each are enclosed by fencing the perimeter of the rectangular lot which includes a fence across the middle.

Consider the perimeter of the rectangle is P

Thus, perimeter is P=2(l+b)

The two rectangles have a common side (breadth) which gives the total perimeter for fencing as TP=4l+3b.

In the equation TP=4l+3b, there are two independent variables l and b. Express the equation as a function of one variable by using the provided conditions.

Use the equation for area lb=1200 and make b the subject to get

b=1200l

Apply the equation TP=4l+3b and substitute b=1200l to get

TP=4l+3(1200l)TP=4l+3600l</

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