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\(2x+2y\ge 16\) \(-2x+6y\le 24\) \(-4x+4y\ge -8\) \(f(x,y)=5x+4y\)
@phi think you can help?
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
Perhaps...that's the next lesson I have....
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)
Ah...I'm still watching video lol
Graphing inequalities now...
The next step the dude shows is confusing..."cover up the x"?
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
Okay, the inequalities intersect at (3,5), (9,7), (5,3).
yes. now check each pair
Do I plug them into the equation?
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
Did you do the other 2 pairs?
Minimum is at (3,5) :)
Yes! f(9,7)=73 and f(5,3)=37 :D
That seems easier than I thought it would be...
what did you get for (5,3) ?
dyslexia strikes again!
Mind helping me with a couple more?
It's probably easier than I think it will be...brain isn't working today lol
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
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.
Lol the next ones I have to plot two inequalities and state which numbered region or regions belong to the solution...
After you showed me what to do, that one was pretty easy :)
Thank you, by the way :)