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A rectangular area needs to be fenced in such that fencing on one side costs $15 per meter while the other three cost $10 per meter. The owner of the land has $500 to spend. a. Write out the area of the rectangular area in terms of L only. b. What is the value of L so that the area to be fenced in is L maximal? W

A rectangular area needs to be fenced in such that fencing on one side costs $15 per meter while the other three cost $10 per meter. The owner of the land has $500 to spend. a. Write out the area of the rectangular area in terms of L only. b. What is the value of L so that the area to be fenced in is L maximal? W

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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Question
**Problem 3:** A rectangular area needs to be fenced in such that fencing on one side costs $15 per meter while the other three sides cost $10 per meter. The owner of the land has $500 to spend. a. Write out the area of the rectangular area in terms of \( L \) only. b. What is the value of \( L \) so that the area to be fenced in is maximal? **Diagram Description:** The diagram illustrates a rectangle labeled with dimensions \( L \) (length) and \( W \) (width). The side \( L \) is vertical, and \( W \) is horizontal. Note: The problem involves determining how to express the area of the rectangle in terms of \( L \) and finding the optimal \( L \) to maximize the area, given the constraints on fencing costs.
Transcribed Image Text:**Problem 3:** A rectangular area needs to be fenced in such that fencing on one side costs $15 per meter while the other three sides cost $10 per meter. The owner of the land has $500 to spend. a. Write out the area of the rectangular area in terms of \( L \) only. b. What is the value of \( L \) so that the area to be fenced in is maximal? **Diagram Description:** The diagram illustrates a rectangle labeled with dimensions \( L \) (length) and \( W \) (width). The side \( L \) is vertical, and \( W \) is horizontal. Note: The problem involves determining how to express the area of the rectangle in terms of \( L \) and finding the optimal \( L \) to maximize the area, given the constraints on fencing costs.
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