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A property owner wants to fence a rectar next to the road must be sturdier and cos per foot. The garden is to have an area ot a) Find a function that models the co b) Find the garden dimensions that r c) If the owner has at most $600 to s dimensions that they can build.

A property owner wants to fence a rectar next to the road must be sturdier and cos per foot. The garden is to have an area ot a) Find a function that models the co b) Find the garden dimensions that r c) If the owner has at most $600 to s dimensions that they can build.

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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13. A property owner wants to fence a rectangular garden plot adjacent to a road. The fencing next to the road must be sturdier and costs $5 per foot, but the other fencing costs just $3 per foot. The garden is to have an area of 1200 ft2. a) Find a function that models the cost of fencing the garden. b) Find the garden dimensions that minimize the cost of fencing. c) If the owner has at most $600 to spend on fencing, find the range of fence dimensions that they can build. 14. The profit function for a company selling x units of a certain commodity is given by P(x) = -1500 + 12x -0.0004x2 When will the profit exceed $50,000? Show a graph that will help you solve this. 15. You want to put a fence around a rectangular field and then subdivide the field into 4 smaller rectangular plots by placing three fences parallel to one of the sides. If you can only afford 2000 yards of fencing, what dimensions will give the maximum rectangular area?
Transcribed Image Text:13. A property owner wants to fence a rectangular garden plot adjacent to a road. The fencing next to the road must be sturdier and costs $5 per foot, but the other fencing costs just $3 per foot. The garden is to have an area of 1200 ft2. a) Find a function that models the cost of fencing the garden. b) Find the garden dimensions that minimize the cost of fencing. c) If the owner has at most $600 to spend on fencing, find the range of fence dimensions that they can build. 14. The profit function for a company selling x units of a certain commodity is given by P(x) = -1500 + 12x -0.0004x2 When will the profit exceed $50,000? Show a graph that will help you solve this. 15. You want to put a fence around a rectangular field and then subdivide the field into 4 smaller rectangular plots by placing three fences parallel to one of the sides. If you can only afford 2000 yards of fencing, what dimensions will give the maximum rectangular area?
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