dinorap1
  • dinorap1
Help me out with this linear programming problem please! I will post the question as a screenshot below!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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dinorap1
  • dinorap1
This is the question I need help with. Please help!
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jim_thompson5910
  • jim_thompson5910
`The production of y can exceed x by no more than 200` translates to what inequality?
dinorap1
  • dinorap1
That's what's stumping me here... I'm not sure how to write that one out.

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jim_thompson5910
  • jim_thompson5910
it would translate to `y <= x+200` basically `x+200` is the ceiling or max value for y. It can't go any higher
jim_thompson5910
  • jim_thompson5910
also, it's implicitly stated that `x >= 0` and `y >= 0` since x and y are the number of products made
dinorap1
  • dinorap1
Oh okay. So now all I have to do is write it out on a graph and plug the vertices into the equation?
jim_thompson5910
  • jim_thompson5910
so what you need to do is graph this system of inequalities \[\Large \begin{cases}y \le x+200\\ x+2y \le 1600\\ x \ge 0\\ y \ge 0\end{cases}\]
jim_thompson5910
  • jim_thompson5910
find the shaded feasible region and the corner points of that region. Then plug each corner point into the profit function
dinorap1
  • dinorap1
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...
jim_thompson5910
  • jim_thompson5910
sure I can do that
dinorap1
  • dinorap1
Alright I'm almost done graphing it...
jim_thompson5910
  • jim_thompson5910
ok
dinorap1
  • dinorap1
Here's what it looks like...
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jim_thompson5910
  • jim_thompson5910
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
dinorap1
  • dinorap1
So my graph doesn't look right yet...?
dinorap1
  • dinorap1
Now it looks like this. :/
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jim_thompson5910
  • jim_thompson5910
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
jim_thompson5910
  • jim_thompson5910
yeah that looks better. if you focus on the region where all 4 graphs have in common, you'll have this region here
dinorap1
  • dinorap1
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?
jim_thompson5910
  • jim_thompson5910
each corner point is found by finding the intersection of the lines
jim_thompson5910
  • jim_thompson5910
example: (0,200) is found by finding the intersection of the lines `x = 0` and `y=x+200`
dinorap1
  • dinorap1
I'm getting a little confused... x>=0 isn't a line, is it? It just prevents x from equalling 0 I thought...
dinorap1
  • dinorap1
Same with y>=0
jim_thompson5910
  • jim_thompson5910
`x = 0` is the boundary line to `x >= 0`
jim_thompson5910
  • jim_thompson5910
`x = 0` is the y axis `x >= 0` means you shade to the right of the y axis
dinorap1
  • dinorap1
Okay I think the answer is C, which is: (1600,0) Is that right?
dinorap1
  • dinorap1
I need to go really soon
jim_thompson5910
  • jim_thompson5910
yep the profit is P = 21500 at (x,y) = (1600,0) which is the max profit
dinorap1
  • dinorap1
Okay I'm about to submit it then... hope I don't get a crappy grade! I've been working on this for hours!
dinorap1
  • dinorap1
I got a 3/3! Thank you for helping! You really helped me understand this better! :)

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