Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

fa272 Group Title

minimize f(x)=(x1-2)^2+(x2-5)^2 subject to g1=-x1-x2+10<=0 and g2=-2x1+3x2-10<=0

  • one year ago
  • one year ago

  • This Question is Closed
  1. fa272 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    It's under the single objective optimization problem

    • one year ago
  2. facemash-RNC Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I dont get you

    • one year ago
  3. fa272 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Why? is the question not clear?

    • one year ago
  4. fa272 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Can anyone help me?

    • one year ago
  5. fa272 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I need the steps o solve the problem

    • one year ago
  6. JakeV8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Make a coordinate axis "thing" with vertical axis as "x2" and horizontal as "x1". For each of the two constraints, simplify so that you solve for x2 on one side, and the form will be like x2 >= mx1 + b so that you can sketch the inequality on your graph. Shade the appropriate region based on the inequality. So this will give you two constraint regions... I think, then, the process is somewhat of an iterative trial and error of looking at x1 and x2 combinations that are "allowable' (meaning they fall into the overlapping regions of the 2 constraints), and choosing the x1,x2 pair that creates the minimum f(x) result.

    • one year ago
  7. JakeV8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    there may be a straight analytical method, but what I have seen in the last few minutes points toward iterative approaches. Not my favorite, but maybe that's the right idea here.

    • one year ago
  8. fa272 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    isn't the f(x) result a single number or a coordinate point (x,y)?

    • one year ago
  9. JakeV8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yes, I think... it is a single number result based on the inputs (x1, x2)

    • one year ago
  10. fa272 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    you mean the final number will be the intersetion between the two lines?

    • one year ago
  11. JakeV8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1348759891533:dw|

    • one year ago
  12. JakeV8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    No, the f(x) value is the single value that results from choosing x1 and x2 inputs from the shaded region above, plugging them into the f(x) expression, and just getting the number result. But different choices of x1 and x2 give different f(x) results... you need to find the x1 and x2 that give the SMALLEST (i.e. minimum) f(x) result.

    • one year ago
  13. JakeV8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    just for fun, it looks like x1 = 20, x2 = 0 falls in the allowed region. So... f(x)=(x1-2)^2+(x2-5)^2 f(x) = (20-2)^2 + (0-5)^2 = 18^2 Or you could try x = 21, x2 = 0 -->> f(x) = 19^2 so that's bigger, and not the minimum... better try searching smaller values of x1 and x2, but you can only choose from within the constraint region.

    • one year ago
  14. fa272 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    the constraint regionis the shaded part on the right?

    • one year ago
  15. JakeV8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yes, the constraint region is the shaded area that satisfies both g1 and g2 constraint inequalities Another point I just checked is the point where the two constraint lines hit the x2 vertical axis is (x1,x2) = (0,10) f(x) at that point is (0-2)^2 + (10-5)^2 = 4 + 25 = 29 this is much better than 19^2, but still may not be the minimum f(x)

    • one year ago
  16. fa272 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    so do I just guess some points for f(x) to get the smallest number that fits in the shaded area?

    • one year ago
  17. JakeV8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    well, that's the part that I don't really like, but yeah, I think that's the approach. But don't just guess randomly... think about closing in on the target... like a kid's game of finding a lost object with "hotter, colder' responses... adjust your next guess to take advantage of the results of your last guess. My intuition is that the minimum f(x) will result from an x1, x2 pair that is very close to the left side of the shaded region. However, because the two inputs cause different "contributions" to the overall f(x), it could be that choosing the smallest x1 is NOT the best choice... maybe choosing a bigger x1 than 0 will allow a smaller x2 choice which will then lead to a lower overall f(x) value.

    • one year ago
  18. JakeV8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    So (0,10) is one guess, but also try some points where x1 is not 0... small steps to the right, and maybe downward from (0,10), like (1,9)... just be sure to stay inside the shaded region

    • one year ago
  19. JakeV8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    If you are struggling at all with what this optimization means, an easy example might be: f(x) is my # of questions missed on the exam. I want to minimize f(x). f(x) is some function that depends on "hours studied" and "hours of sleep". I can maximize my study hours if I study 24 hours a day, which then makes sleep necessarily zero, but this may or may not optimize (meaning minimize) my "# of questions missed" score. Then again, I could sleep 24 hours a day and study none, and I might score well, but I doubt it. I need to choose the optimum study/sleep balance to minimize my missed questions.

    • one year ago
  20. fa272 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I got the idea ... I just want to make sure I understand the steps: first I take the constraints and make them equal to either x1 or x2 second I'll plug numbers for each constraint equation to form a line and get the area where the solution exists third I take the f(x) equation and solve it for different numbers under th area to find the minimum solution Is this correct?

    • one year ago
  21. JakeV8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I think you got it... the way you phrased your first step confuses me a bit, but if you're saying basically "graph the inequalities represented by the constraints", that's it.

    • one year ago
  22. JakeV8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    don't let the g1 and g2 confuse you... think of those as labels or names... "constraint # 1" and "constraint # 2" The actual constraint is an inequality using 2 variables, x1, and x2... for convention, I would treat x2 like the y variable in a normal x-y graph (i.e. make x2 the vertical axis)

    • one year ago
  23. JakeV8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Is this for an engineering class? Or straight math?

    • one year ago
  24. fa272 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    engineering class

    • one year ago
  25. JakeV8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I found a PDF handout from a Purdue site online a bit ago... had to teach myself this stuff too :) It's attached if you want it for reference... it's more broad than just this one question, but it might be helpful.

    • one year ago
  26. fa272 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Thanks that is helpful. Sorry if I'm asking too many questions but do you know how it can be programmed in Matlab?

    • one year ago
  27. JakeV8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I don't mind questions... love to help, plus I learned something also :) but unfortunately, I don't know Matlab at all... would love to help but that's not an area I can do. You might rephrase the question to focus on "how to program in matlab" and re-post it as a new question... might get some fresh help from someone with Matlab skills. Also, I think there are some engineering forums too... might "cross post" it in one of those if you find one that looks promising.

    • one year ago
  28. fa272 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Thank you so much for your help... I really appreciate it. This is my first time in this site, so I'm trying to learn the interface and features around here too :)

    • one year ago
  29. JakeV8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    good luck with the site... btw, you can "join" multiple areas... look at the blue bar over "ask a question" and choose "find more subjects"... you can add physics or engineering or whatever without quitting the math page... you can jump back and forth quickly and get updates on both. I'm pretty new to this too, but it seems to work well. Lots of early math questions here though... I think there are a lot of home school and online school kids asking some really basic stuff, and worse, some are just wanting someone to hand them answers. I am glad you were willing to take the time to try to learn this optimization... it was refreshing to help with a problem that made me think pretty hard :)

    • one year ago
  30. JakeV8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    also, for what it's worth, you can reward people who help you by clicking the little "best response' button beside the person's response in the thread above... that gives them a "medal" for helping, which adds to their score and helps identify them as someone who is generally trustworthy for help... i.e., better to get help from a "99" guy than a "6" guy... if the 6 guy is really good, he'll get medals and "move up the charts" in his score... score is like "math cred"

    • one year ago
  31. JakeV8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Except I have no idea how long it takes to get up to a 99!!! I have helped a bunch and my rate of change of score is slowing :) Fast progress at the start

    • one year ago
  32. fa272 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I just reliazed I have another question, what if I happen to have two f(x) f (x)= (x1-2)^2 + (x2-5)^2 f(x) = (x1-4.5)^2 + (x2-8.5)^2 with the same constraints is it the same process?

    • one year ago
  33. JakeV8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    but it's taken a week to go from like 60 to 64

    • one year ago
  34. JakeV8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    What is the actual question on that one? Is it minimize f(x)?

    • one year ago
  35. fa272 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yes minimize

    • one year ago
  36. JakeV8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Yeah, it should be the same process, but I am confused a little by how you can name a function f(x), define it in terms of the inputs, and then name a separate function the same name f(x) but give it a different definition in terms of the inputs. Algebra would say f(x) = f(x), meaning the 2 expressions should be equivalent, but at a quick glance, they don't appear to be. I would just follow the same process of finding the min f(x) using the x1 and x2 constraint region... do it once for the first f(x), and then repeat for the 2nd f(x).... basically find min f(x) on the first expression, then min f(x) using the 2nd expression, as if it was 2 separate problems. But that's a weird way to ask it... I wonder if I'm missing something... (?)

    • one year ago
  37. fa272 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yeah sorry the first is f1(x) and the other is f2(x)

    • one year ago
  38. JakeV8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Are you supposed to minimize each one individually? Or somehow deal with them both together?

    • one year ago
  39. fa272 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    it says in the book that they used the pareto optimal set but don't know what it means and they don't solve these equations mathmatically.

    • one year ago
  40. fa272 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    attached is the graph that is suppose to be for this problem and I need to know how they ended up drawing it like this

    • one year ago
    1 Attachment
  41. fa272 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I think we need to deal with them together because it's mentioned under two objective optimization problem

    • one year ago
  42. fa272 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    This is the link for the book: http://caemm.zxq.net/em503/EM503%20-%20Introduction%20to%20Optimum%20Design%20-%20Jasbir%20Arora%20-%202%20ed.pdf and it's in chapter 17

    • one year ago
  43. JakeV8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yep, I agree... unfortunately, you just moved past where I have much idea. I'll read about it, but at this point, I'm like someone walking into your class mid-term and trying to catch up :) one last thing for now: notice that the plot in that picture is f2 vs. f1, so as you put in x1 and x2 values, you generate f2 and f1 results, which you could then plot against each other like they did in that drawing. Doing this by hand will start to be a serious pain though... a tool would be very useful (Matlab) Thanks for the textbook link... I will read up on it, but it will take me a bit and I have to log off here in a few minutes... I will check back later.

    • one year ago
  44. fa272 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    ok.. thanks for your help... appreciate your time :)

    • one year ago
  45. JakeV8 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    It was interesting... makes me wish I had taken this class :) Good luck!

    • one year ago
  46. fa272 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Thank you

    • one year ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.