Find the minimum value of the function for the polygonal convex set determined by the given system of inequalities. Please no direct answers.

- haleyelizabeth2017

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- haleyelizabeth2017

\(2x+2y\ge 16\)
\(-2x+6y\le 24\)
\(-4x+4y\ge -8\)
\(f(x,y)=5x+4y\)

- haleyelizabeth2017

@phi think you can help?

- aaronq

I dont really remember how to do this and i dont want to give you a crappy answer, buti think this video may be helpful
https://www.youtube.com/watch?v=RPuhkQ0vGK0

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## More answers

- haleyelizabeth2017

Perhaps...that's the next lesson I have....

- phi

How far did you get? I think you plot the relations, and find the intersection points
then at each intersection point, evaluate the function f(x,y)

- haleyelizabeth2017

Ah...I'm still watching video lol

- haleyelizabeth2017

Graphing inequalities now...

- haleyelizabeth2017

The next step the dude shows is confusing..."cover up the x"?

- phi

I used geogebra to plot them

##### 1 Attachment

- haleyelizabeth2017

okay

- phi

that is the hard part, finding the intersection points
once you have them, you have (x,y) pairs that you "evaluate" using
f(x,y) = 5x+4y

- haleyelizabeth2017

Okay, the inequalities intersect at (3,5), (9,7), (5,3).

- phi

yes. now check each pair

- haleyelizabeth2017

Do I plug them into the equation?

- phi

yes.

- haleyelizabeth2017

f(3,5)=35

- phi

at every point on the graph f(x,y) has a value. But the max or min values will always occur at one of the vertexes (intersection points of the boundaries)
so we test each vertex. One will be the min and that is the pair we pick

- haleyelizabeth2017

Ah hah

- phi

Did you do the other 2 pairs?

- haleyelizabeth2017

Minimum is at (3,5) :)

- haleyelizabeth2017

Yes! f(9,7)=73 and f(5,3)=37 :D

- haleyelizabeth2017

That seems easier than I thought it would be...

- phi

what did you get for (5,3) ?

- haleyelizabeth2017

37....

- phi

dyslexia strikes again!

- haleyelizabeth2017

aw

- haleyelizabeth2017

Mind helping me with a couple more?

- haleyelizabeth2017

It's probably easier than I think it will be...brain isn't working today lol

- phi

no, my brain was not working and I confused 5,3 and 3,5
but yes, the answer is at 3,5
they want Find the minimum value of the function , so 35 is the answer

- phi

The painful part of these problems is plotting the relations, and finding the intersection points. If you can use something like geogebra or other such tools, then the problems are not too hard.

- haleyelizabeth2017

Lol the next ones I have to plot two inequalities and state which numbered region or regions belong to the solution...

- haleyelizabeth2017

After you showed me what to do, that one was pretty easy :)

- haleyelizabeth2017

Thank you, by the way :)

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