## anonymous one year ago Help me out with this linear programming problem please! I will post the question as a screenshot below!

1. anonymous

2. jim_thompson5910

The production of y can exceed x by no more than 200 translates to what inequality?

3. anonymous

That's what's stumping me here... I'm not sure how to write that one out.

4. 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

5. jim_thompson5910

also, it's implicitly stated that x >= 0 and y >= 0 since x and y are the number of products made

6. anonymous

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

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

find the shaded feasible region and the corner points of that region. Then plug each corner point into the profit function

9. anonymous

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

sure I can do that

11. anonymous

Alright I'm almost done graphing it...

12. jim_thompson5910

ok

13. anonymous

Here's what it looks like...

14. 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

15. anonymous

So my graph doesn't look right yet...?

16. anonymous

Now it looks like this. :/

17. 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

18. 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

19. anonymous

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

each corner point is found by finding the intersection of the lines

21. jim_thompson5910

example: (0,200) is found by finding the intersection of the lines x = 0 and y=x+200

22. anonymous

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

23. anonymous

Same with y>=0

24. jim_thompson5910

x = 0 is the boundary line to x >= 0

25. jim_thompson5910

x = 0 is the y axis x >= 0 means you shade to the right of the y axis

26. anonymous

Okay I think the answer is C, which is: (1600,0) Is that right?

27. anonymous

I need to go really soon

28. jim_thompson5910

yep the profit is P = 21500 at (x,y) = (1600,0) which is the max profit

29. anonymous

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. anonymous

I got a 3/3! Thank you for helping! You really helped me understand this better! :)