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dinorap1

  • one year ago

Help me out with this linear programming problem please! I will post the question as a screenshot below!

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  1. dinorap1
    • one year ago
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    This is the question I need help with. Please help!

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  2. jim_thompson5910
    • one year ago
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    `The production of y can exceed x by no more than 200` translates to what inequality?

  3. dinorap1
    • one year ago
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    That's what's stumping me here... I'm not sure how to write that one out.

  4. jim_thompson5910
    • one year ago
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    it would translate to `y <= x+200` basically `x+200` is the ceiling or max value for y. It can't go any higher

  5. jim_thompson5910
    • one year ago
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    also, it's implicitly stated that `x >= 0` and `y >= 0` since x and y are the number of products made

  6. dinorap1
    • one year ago
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    Oh okay. So now all I have to do is write it out on a graph and plug the vertices into the equation?

  7. jim_thompson5910
    • one year ago
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    so what you need to do is graph this system of inequalities \[\Large \begin{cases}y \le x+200\\ x+2y \le 1600\\ x \ge 0\\ y \ge 0\end{cases}\]

  8. jim_thompson5910
    • one year ago
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    find the shaded feasible region and the corner points of that region. Then plug each corner point into the profit function

  9. dinorap1
    • one year ago
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    Oh wow, thanks for writing it like that! That helps a lot! :D I have a graphing tool that does it for me. Maybe you can look at it after I'm done to see if I'm doing it right...

  10. jim_thompson5910
    • one year ago
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    sure I can do that

  11. dinorap1
    • one year ago
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    Alright I'm almost done graphing it...

  12. jim_thompson5910
    • one year ago
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    ok

  13. dinorap1
    • one year ago
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    Here's what it looks like...

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  14. jim_thompson5910
    • one year ago
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    don't forget x >= 0 and y >= 0 when you graph all 4 inequalities and focus on the region where all shaded regions overlap, you'll get this

  15. dinorap1
    • one year ago
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    So my graph doesn't look right yet...?

  16. dinorap1
    • one year ago
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    Now it looks like this. :/

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  17. jim_thompson5910
    • one year ago
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    it's a mess when you do all 4 graphs at the same time https://www.desmos.com/calculator/wpwycrhycx but with the link above, you can turn on/off graphs so you can see them individually or grouped

  18. jim_thompson5910
    • one year ago
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    yeah that looks better. if you focus on the region where all 4 graphs have in common, you'll have this region here

  19. dinorap1
    • one year ago
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    That looks much better than my graph. I still know the general area where all the vertices are, so I can probably deal with it looking messy like this... is my graph still accurate besides that?

  20. jim_thompson5910
    • one year ago
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    each corner point is found by finding the intersection of the lines

  21. jim_thompson5910
    • one year ago
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    example: (0,200) is found by finding the intersection of the lines `x = 0` and `y=x+200`

  22. dinorap1
    • one year ago
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    I'm getting a little confused... x>=0 isn't a line, is it? It just prevents x from equalling 0 I thought...

  23. dinorap1
    • one year ago
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    Same with y>=0

  24. jim_thompson5910
    • one year ago
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    `x = 0` is the boundary line to `x >= 0`

  25. jim_thompson5910
    • one year ago
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    `x = 0` is the y axis `x >= 0` means you shade to the right of the y axis

  26. dinorap1
    • one year ago
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    Okay I think the answer is C, which is: (1600,0) Is that right?

  27. dinorap1
    • one year ago
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    I need to go really soon

  28. jim_thompson5910
    • one year ago
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    yep the profit is P = 21500 at (x,y) = (1600,0) which is the max profit

  29. dinorap1
    • one year ago
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    Okay I'm about to submit it then... hope I don't get a crappy grade! I've been working on this for hours!

  30. dinorap1
    • one year ago
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    I got a 3/3! Thank you for helping! You really helped me understand this better! :)

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