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A postal service will accept packages only if the length plus girth is no more than 276 inches. (See the figure.) Length Girth Assuming that the front face of the package (as shown in the figure) is square, what is the largest volume ackage that the postal service will accept? in 3

A postal service will accept packages only if the length plus girth is no more than 276 inches. (See the figure.) Length Girth Assuming that the front face of the package (as shown in the figure) is square, what is the largest volume ackage that the postal service will accept? in 3

Advanced Engineering Mathematics
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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**Problem Description:** A postal service will accept packages only if the length plus girth is no more than 276 inches. (See the figure.) **Diagram Explanation:** The diagram shows a rectangular prism (box) where: - The **front face** of the package is square, indicating that the width and height of this face are equal. - **Girth** is represented by the perimeter of the cross-section (the square face) excluding the length. Essentially, in this context, girth is twice the width plus twice the height, which simplifies to four times the side length of the square face. - **Length** is the dimension perpendicular to the square face. **Question:** Assuming that the front face of the package (as shown in the figure) is square, what is the largest volume package that the postal service will accept? **Solution Approach:** 1. Identify the variables: - Let \( s \) be the side of the square front face. - Let \( l \) be the length of the package. 2. Express the condition: - The postal service condition is: \( l + 4s \leq 276 \). 3. Express the volume: - Volume \( V = s^2 \times l \). 4. Objective: - Maximize the volume given the constraint on length and girth. Find the values of \( s \) and \( l \) that satisfy the constraint and maximize the volume. Enter your calculated volume in the box provided.
Transcribed Image Text:**Problem Description:** A postal service will accept packages only if the length plus girth is no more than 276 inches. (See the figure.) **Diagram Explanation:** The diagram shows a rectangular prism (box) where: - The **front face** of the package is square, indicating that the width and height of this face are equal. - **Girth** is represented by the perimeter of the cross-section (the square face) excluding the length. Essentially, in this context, girth is twice the width plus twice the height, which simplifies to four times the side length of the square face. - **Length** is the dimension perpendicular to the square face. **Question:** Assuming that the front face of the package (as shown in the figure) is square, what is the largest volume package that the postal service will accept? **Solution Approach:** 1. Identify the variables: - Let \( s \) be the side of the square front face. - Let \( l \) be the length of the package. 2. Express the condition: - The postal service condition is: \( l + 4s \leq 276 \). 3. Express the volume: - Volume \( V = s^2 \times l \). 4. Objective: - Maximize the volume given the constraint on length and girth. Find the values of \( s \) and \( l \) that satisfy the constraint and maximize the volume. Enter your calculated volume in the box provided.
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