haleyelizabeth2017
  • haleyelizabeth2017
Find the minimum value of the function for the polygonal convex set determined by the given system of inequalities. Please no direct answers.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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haleyelizabeth2017
  • haleyelizabeth2017
\(2x+2y\ge 16\) \(-2x+6y\le 24\) \(-4x+4y\ge -8\) \(f(x,y)=5x+4y\)
haleyelizabeth2017
  • haleyelizabeth2017
@phi think you can help?
aaronq
  • 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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haleyelizabeth2017
  • haleyelizabeth2017
Perhaps...that's the next lesson I have....
phi
  • 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
  • haleyelizabeth2017
Ah...I'm still watching video lol
haleyelizabeth2017
  • haleyelizabeth2017
Graphing inequalities now...
haleyelizabeth2017
  • haleyelizabeth2017
The next step the dude shows is confusing..."cover up the x"?
phi
  • phi
I used geogebra to plot them
1 Attachment
haleyelizabeth2017
  • haleyelizabeth2017
okay
phi
  • 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
  • haleyelizabeth2017
Okay, the inequalities intersect at (3,5), (9,7), (5,3).
phi
  • phi
yes. now check each pair
haleyelizabeth2017
  • haleyelizabeth2017
Do I plug them into the equation?
phi
  • phi
yes.
haleyelizabeth2017
  • haleyelizabeth2017
f(3,5)=35
phi
  • 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
  • haleyelizabeth2017
Ah hah
phi
  • phi
Did you do the other 2 pairs?
haleyelizabeth2017
  • haleyelizabeth2017
Minimum is at (3,5) :)
haleyelizabeth2017
  • haleyelizabeth2017
Yes! f(9,7)=73 and f(5,3)=37 :D
haleyelizabeth2017
  • haleyelizabeth2017
That seems easier than I thought it would be...
phi
  • phi
what did you get for (5,3) ?
haleyelizabeth2017
  • haleyelizabeth2017
37....
phi
  • phi
dyslexia strikes again!
haleyelizabeth2017
  • haleyelizabeth2017
aw
haleyelizabeth2017
  • haleyelizabeth2017
Mind helping me with a couple more?
haleyelizabeth2017
  • haleyelizabeth2017
It's probably easier than I think it will be...brain isn't working today lol
phi
  • 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
  • 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
  • haleyelizabeth2017
Lol the next ones I have to plot two inequalities and state which numbered region or regions belong to the solution...
haleyelizabeth2017
  • haleyelizabeth2017
After you showed me what to do, that one was pretty easy :)
haleyelizabeth2017
  • haleyelizabeth2017
Thank you, by the way :)

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