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

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

Mathematics
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This is the question I need help with. Please help!
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`The production of y can exceed x by no more than 200` translates to what inequality?
That's what's stumping me here... I'm not sure how to write that one out.

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

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