Question

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

Answer 1

This is the question I need help with. Please help!

Answer 2

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

Answer 3

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

Answer 4

it would translate to `y <= x+200`

basically `x+200` is the ceiling or max value for y. It can't go any higher

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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...

Answer 10

sure I can do that

Answer 11

Alright I'm almost done graphing it...

Answer 12

ok

Answer 13

Here's what it looks like...

Answer 14

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

Answer 15

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

Answer 16

Now it looks like this. :/

Answer 17

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

Answer 18

yeah that looks better. if you focus on the region where all 4 graphs have in common, you'll have this region here

Answer 19

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?

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

Same with y>=0

Answer 24

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

Answer 25

`x = 0` is the y axis

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

Answer 26

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

Answer 27

I need to go really soon

Answer 28

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

Answer 29

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

Answer 30

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