Find the minimum cost of a rectangular box of volume 100 cm³ whose top and bottom cost 2 cents per cm² and whose sides cost 8 cents per cm². Round your answer to nearest whole number cents. Cost = cents.
Find the minimum cost of a rectangular box of volume 100 cm³ whose top and bottom cost 2 cents per cm² and whose sides cost 8 cents per cm². Round your answer to nearest whole number cents. Cost = cents.
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 Statement:**
Find the minimum cost of a rectangular box of volume 100 cm³ whose top and bottom cost 2 cents per cm² and whose sides cost 8 cents per cm². Round your answer to the nearest whole number of cents.
**Solution Representation:**
Cost = [Input Box] cents.
---
To solve this problem, you need to:
1. Define the dimensions of the box (length, width, and height).
2. Express the cost in terms of these dimensions, considering the different costs for the top, bottom, and sides.
3. Use the constraint of the box's volume (100 cm³) to relate the dimensions.
4. Optimize the cost function to find the minimum cost, rounding to the nearest whole number of cents.
This problem involves calculus or algebraic techniques to find the optimal solution for minimum cost.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8216494-bf6c-44b6-949f-dd8ff9f3594a%2Fa8e705b8-8bcf-445e-b41f-6ad60b422670%2Fymr58vd_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the minimum cost of a rectangular box of volume 100 cm³ whose top and bottom cost 2 cents per cm² and whose sides cost 8 cents per cm². Round your answer to the nearest whole number of cents.
**Solution Representation:**
Cost = [Input Box] cents.
---
To solve this problem, you need to:
1. Define the dimensions of the box (length, width, and height).
2. Express the cost in terms of these dimensions, considering the different costs for the top, bottom, and sides.
3. Use the constraint of the box's volume (100 cm³) to relate the dimensions.
4. Optimize the cost function to find the minimum cost, rounding to the nearest whole number of cents.
This problem involves calculus or algebraic techniques to find the optimal solution for minimum cost.
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