   Chapter 10.4, Problem 18E ### 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 cost From a tract of land a developer plans to fence a rectangular region and then divide it into two identical rectangular lots by putting a fence down the middle. Suppose that the fence for the outside boundary costs $5 per foot and the fence for the middle costs$2 per foot. If each lot contains 13,500 square feet, find the dimensions of each lot that yield the minimum cost for the fence.

To determine

To calculate: The dimensions to minimize the costs if both rectangular fields contain 13,500 sq.ft each.

Explanation

Given Information:

Two fields contain 13,500 sq.ft each when fencing is done at the cost of $5 per foot for the outside boundary and at$2 per foot for the fencing at the middle that partitions the two fields.

Formula used:

To find the minimum 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 more than zero, then substituting the value of the independent variable will give the minimum 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:

Consider the provided statement,

Both rectangular fields contain 13,500 sq.ft each when fencing is done at the cost of $20 per foot for the outside boundary and at$8 per foot for the fencing at the middle that partitions the two fields.

Assume, the perimeter of the rectangular field is P

So, the perimeter P=2l+2b. The cost for fencing is C=5(2l+2b)+2b.

In the equation C=5(2l+2b)+2b, there are two independent variables l and b. Express the equation as a function of one variable by using the provided conditions.

Area of rectangle is A=lb

Use the equation for area lb=13500 and make b the subject to get

b=13500l

Apply the equation C=5(2l+2b)+2b and substitute b=13500l to get

C=10

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Define sampling with replacement and explain why is it used?

Statistics for The Behavioral Sciences (MindTap Course List)

#### For and

Study Guide for Stewart's Multivariable Calculus, 8th

#### True or False: converges.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 