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

Question

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

haleyelizabeth2017 · Answer

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

haleyelizabeth2017 · Answer

@phi think you can help?

aaronq · Answer

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

haleyelizabeth2017 · Answer

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

phi · Answer

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 · Answer

Ah...I'm still watching video lol

haleyelizabeth2017 · Answer

Graphing inequalities now...

haleyelizabeth2017 · Answer

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

phi · Answer

I used geogebra to plot them

haleyelizabeth2017 · Answer

okay

phi · Answer

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 · Answer

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

phi · Answer

yes.  now check each pair

haleyelizabeth2017 · Answer

Do I plug them into the equation?

phi · Answer

yes.

haleyelizabeth2017 · Answer

f(3,5)=35

phi · Answer

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 · Answer

Ah hah

phi · Answer

Did you do the other 2 pairs?

haleyelizabeth2017 · Answer

Minimum is at (3,5) :)

haleyelizabeth2017 · Answer

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

haleyelizabeth2017 · Answer

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

phi · Answer

what did you get for (5,3) ?

haleyelizabeth2017 · Answer

37....

phi · Answer

dyslexia strikes again!

haleyelizabeth2017 · Answer

aw

haleyelizabeth2017 · Answer

Mind helping me with a couple more?

haleyelizabeth2017 · Answer

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

phi · Answer

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 · Answer

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 · Answer

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

haleyelizabeth2017 · Answer

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

haleyelizabeth2017 · Answer

Thank you, by the way :)