# Tag Info

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Here's the example I had which inspired me to post the question in the first place: The game League of Legends was the most-played PC game, in number of hours played, in North America and Europe in 2012. There is a good chance that League of Legends is a part of many of your students' daily life, especially if you are teaching engineering calculus. It doesn'...

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Bad Optimization Problems I thought that Jack M made an interesting comment about this question: There aren't any. There may be situations where it's possible to apply optimization to solve a problem you've encountered, but in none of these cases is it honestly worth the effort of solving the problem analytically. I optimize path lengths every day when I ...

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When someone swallows a dose of a drug, it doesn't go into their bloodstream all at once. What will the drug's peak blood concentration be, and when will it be reached? If the drug is caffeine, which is absorbed and eliminated by first-order kinetics, its blood concentration $c$ rises and falls over time along the curve c(t) = \tfrac{D}{1-\beta/\alpha}\...

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This is from a post of mine on Math Stackexchange. When I was in college, I owned three lamps and had a dark apartment. I kept trying to position them in different areas of the room, but it was still dark. Then I decided to model the problem with math: given three light sources of equal strength in a rectangular solid of a room, where can you place them to ...

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As I mentioned in my other answer, it highly depends what is meant by their lives. Here is a every day problem which I, at least, often encounter: If you do the dishes and finish, there is a lot of foam in your sink. Arrange the position and strength of the water-tap in order to let the foam disappear as fast as possible. The problem sounds easy, but is ...

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An answer depends on what you mean with their lives. I think, it is more likely that students will face such problems in their working (not academic) life. The Netflix Prize example My example is the Netflix Prize, which was awarded by Netflix in the mid 2000s. At that time, Netflix was a DVD rental service and users did rate the movies they have seen. ...

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The original classic real-life example is to lay out a shop floor with multiple workstations and workers, so as to minimize travel distance of the work piece given a required sequence of operations. This can be generalized to consider a standard work load distributed amongst more than one type of workpiece, with different sequences of operations, and ...

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Can't believe no one's mentioned the coke-can problem! You are the designer of drinks cans for Coke, how can you make them the most money? Pretty quickly it comes out that you want a cylinder of volume 330ml with minimal surface area (use the least metal possible to enclose your beverage). It's a classic problem and one kids can very easily relate to on ...

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Edit (4/29/14): A popular media piece in the New York Times on rent division gives a great example of how Sperner's Lemma can be used for fair division problems (as related to cake cutting, the history of which can be found in a pasted excerpt at the end of my response here). The AMM article drawn upon is: Su, F. E. (1999). Rental Harmony: Sperner's Lemma ...

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Determine the minimum distance from a parametric equation $(x(t), y(t))$ to a given point $(x_0, y_0)$. Eg. at which point should a person leave a road (described by the parametric equation), such that the walking distance to the point $(x_0, y_0)$ from the road is minimized? The problem is then: Minimize $\sqrt{(x-x_0)^2 + (y - y_0)^2}$ subject to $x = x(... 8 A lot of examples exist in industry. Manufacturing plants use optimization to figure out how to best run their machinery, buy raw materials, ship finished goods, etc. Airlines and other passenger transportation services use optimization to determine their schedules. The cargo transportation industry (trucking, trains, etc.) uses optimization to determine ... 7 Here's an optimisation problem that really should have solutions readily available, but hasn't: Consider a SatNav that tells you the best way to get from A to B. Now assume the distance is quite long, and you won't be able to get from A to B without going to a petrol station. So what I want: Find the shortest way from A to B visiting any petrol station ... 7 Here's a problem that I found interesting: I listen to audiobooks. When you import them from CD, you get lots of tiny chapters (often 2 or 3 minutes) which is not very practical. Also, audiobooks can be very long - some are 30 hours - which is also not very practical. I prefer audiobooks to be split into individual volumes of not more than 8 hours, and ... 5 This example is maybe the most easy, but in my opinion it does not highlight the necessity to use methods of constrained optimization since the constrained equation is explicitly invertible. A gardener has 20 meters of fence-material and wants to fence a rectangle shaped area with maximal area. The problem reads then as: Maximize$f(a,b)=a\cdot b$... 5 Bankruptcy problems ask for how to "fairly" distribute \$E to honest claimants whose claims exceed the amount \$E. For example,$A$claims \$30, $B$ claims \$50 and$C$claims \$120 and there is only \$160 to distribute. There are two methods dating back to "medieval" times associated with Moses Maimonides. a. Try to equalize the amount given (gain) to each ... 3 How about figuring out the dimensions of a cylindrical can of a specific volume that will minimize the surface area (and therefore minimize the amount of metal material needed to make up the can)? If you've taught calculus, you probably recognize this as one of the classic textbook optimization examples along with fences against barns and picture frames and ... 3 A real-life optimization problem: It takes about 20 clicks and 2 minutes to shoot a wolf. 200 dead wolves will get you enough experience points to get to the next level. It takes about 50 clicks and 10 minutes to steal gold from a palace. 50 burglaries will get you enough experience points to get to the next level. However, you would get carpal tunnel ... 3 Creating a timetable, all students should understand the issues. However mathematical solutions don’t work as well as computer sci solutions. Choosing a set of options, so as to get a degree while having the lease dead time, the dead time being when you are waiting for the next activity to start, but don’t have long enough to do someone useful. In the US ... 2 Profit maximation! It's easy to understand, not so hard to calculate and even testable. Let them sell lemonade or whatever at the next school festival and see, if they can find the optimal price for the lemonade. 2 Following on the example above by Markus Klein: A gardener has 20 meters of fence-material and wants to fence a rectangle shaped garden with maximal area. Furthermore, the garden will be located next to the house such that the house will serve as one of the four walls. The problem then reads: Maximize$f(a,b) = a*b$subject to$2a + b = 20$. The answer$(a ...

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Some simple examples you can try: 1) Maximize the product of $n$ positive numbers, given their sum is one. 2)Maximize entropy of $p_1,\dots, p_n$ (all $p_i>0$, summing to one) that is maximizing $-\sum p_i \log p_i$. 3) More conditions: Maximizing entropy, but with the extra condition that $\sum a_i p_i = \mu$. You can also try introducing ...

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Since you didn't explicitly ask for problems that students should be able to solve, here are some of interest to many engineers: Which shape of the wing of an F1-car maximises downward force? Or which shape of wing of given span maximise the lift of an airplane. Which shape of a rear-view mirror for a car reduces drag? etc. These problems are not ...

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No one has mentioned shopping directly, although various economic optimization problems have appeared in this thread. You have \$20 to spend for your breakfast budget. See how oatmeal (or your favorite breakfast option) is packaged at different prices, whether by single serving envelope, small container at one price, large container at another. What is ...

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Simple. Put a tin of beer on the table and ask the students if the packaging is the optimal solution. i.e. a cylinder has a volume of 500cm^3, what is the minimum possible surface area. Then compare to the actual surface area. I'm doing this in class tomorrow :)

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Why not maximum likelihood estimation (from stats, if you're not familiar with this) in the one-parameter case? You don't need to provide all of the statistical jargon to them. Simply present a formula and ask them to find the value of the parameter which maximizes the parameter. For example, I recently finished teaching Calc. I to a friend of mine. Here's ...

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Many daily life and OR problems take the following form. One has a container of fixed size and a collection of objects each with a value, and size less than that of the container. The goal of the optimization is to decide what items to take which maximizes the value of what gets taken subject to the size constraint. Problems of this kind are known as ...

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