Linear programming: How to find the max/min pt from region?

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Megara2009

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Mar 17, 2007
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I'm in Algebra II and we're doing a chapter with linear programming . My teacher is a great teacher and she's helped me with it for the past three days after school. I "get it" when I'm doing it with her, but it seems like I can't do it on my own.

Does anybody know an easy way to do this sort of exercise? I can do all the way up until you have to find the maximum and minimum. Can anyone help me past that?

Thank you!
 
Actually, if you can do the set-up (extracting the inequalities from the word problems), the graphing (finding the feasibilitiy region), and the finding of coordinates (of the corners of the feasibility region), then the max/min part is easy: Just plug the corner coordinates into your optimization equation, and take the corner(s) that give you the largest and/or smallest value(s).

That's all there is to it! :D

Eliz.
 
Thanks. But, I just tried a problem, and there were only two limits so I only had to lines. Is the feasible region the whole part of the graph where the shading overlaps?
 
Lacking the specifics of the exercise, I'm afraid it will be difficult to provide specific commentary or advice. Sorry.

Eliz.
 
huh. well, I also need to know how to fin the vertices of the point of intersection. My teacher showed my some formula or something like that and I can't follow it.
 
To find where two straight lines intersect, solve each for "y=", and then equate whatever y was equal to.

For instance, to find where y = 3x + 5 and 4x - 2y = 6 intersect, one would solve the second equation for "y=":

. . . . .4x - 2y = 6

. . . . .4x - 6 = 2y

. . . . .2x - 3 = y

Then equate:

. . . . .2x - 3 = 3x + 5

Solve for x. Then back-solve for y. Do this for each set of equations, corresponding to each corner point.

Eliz.
 
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