A country's postal service will accept a package if its length plus its girth (the distance all the way around) does not exceed 84 inches. Find the dimensions (in inches) and volume (in cubic inches) of the largest package with a square base that can be mailed. length base volume girth (distance all the way around) -square base in in x in
A country's postal service will accept a package if its length plus its girth (the distance all the way around) does not exceed 84 inches. Find the dimensions (in inches) and volume (in cubic inches) of the largest package with a square base that can be mailed. length base volume girth (distance all the way around) -square base in in x in
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:**Package Mailing Guidelines**
A country's postal service will accept a package if its length plus its girth (the distance all the way around) does not exceed 84 inches. This task is to find the dimensions (in inches) and volume (in cubic inches) of the largest package with a square base that can be mailed.
**Illustration Explanation**:
The diagram shows a box with a square base. The sides of the square base are equal. The girth is illustrated as a dashed line going around the sides of the box, excluding the top and bottom.
**Calculations Needed**:
- **Length**: The measurement from one end of the package to the other along the longest side.
- **Base**: The side length of the square base of the package.
- **Volume**: Calculated as the base area multiplied by the length.
**Inputs Required**:
- Length: __ in
- Base: __ in
- Volume: __ in³
Using these guidelines, maximize the dimensions so that the girth plus the length does not exceed 84 inches while optimizing the package’s volume.
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