Applied Optimization Problems
The lesson covers various examples of applied optimization problems. The problems involve finding the maximum or minimum value of a given objective function, subject to a constraint or set of constraints. The problems are solved using calculus techniques, such as finding critical numbers, determining concavity, and using optimization formulas. The examples include finding the dimensions of a rectangle inscribed in a parabolic region, finding the dimensions of an aquarium with minimal surface area, finding the height and radius of a cone that can contain a sphere with minimal volume, and finding the point on a curve closest to the origin.
Several example problems of applied optimization.
Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.
- Some Max-Min Problems - Optimization max-min practice problems.
- Where can I find some examples of applied optimization problems?
- How do you maximize the area of a rectangle bounded by a parabola in the first quadrant?
- What is an objective function?
- What is a constraint?
- How do you find the point on a graph that is closest to the origin?
- How do you minimize the surface area of a box?
- How do you minimize the surface area of a can (or right circular cylinder)?
- How can you find the dimensions of a cone with minimum volume that can contain a sphere with radius R?
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Staff Review
This video is a collection of five good applied optimization problems. These problems use ideas and methods we have learned, but they are applied to new situations and word problems. These problems take some really in-depth reasoning, and they are quite difficult and involved. However, they are also very useful and potentially have real-world implications, such as minimizing the construction material for a box or aquarium, minimizing the construction material for a can, and minimizing the volume of a cone.
