Question

SOMEBODY HELP THIS GIRL PLEASE!
Algebra 2 Finals on monday. Help with constraints?!?
Graph each system of constraints. Name all verticies. Then find the values of x and y that maximize the objective formulas find the maximum of minimum values.
I will attach a picture of the problem.

Answer 1

@MathDad72 @EulerGroupie do you think you could help at all?!?

Answer 2

I converted each of the equations to lines of the form y=mx+b and plotted them. When I do, I get a graph that looks a little like this...I think that your answer is in the shaded region (the only area that satisfies all of the constraints). But I'm trying to figure out how to deal with C in the last equation so that we can find a value inside the triangle... hmm...

Answer 3

I might just be unfamiliar with this method of asking the question... might the C mean... "subject to the given constraints"?

Answer 4

5x+y>10
x+y<6
x+4y>12
put 5x+y = 10 ..........(i)
x+y =6 ............(ii)
x+4y =12 ..........(iii)
subtract (ii) from (i)
4x = 4 or x =1 ...........(iv)
subtract (ii) from (iii)
3y = 6
y = 2 ..................(v)
points to check are (2,0),(0,10), (6,0),(0,6), (12,0), (0,3),(1,2)
points does not satisfy are (2,0),(0,10), (6,0) ,(0,6),(12,0)
C=10,000x + 20,000y
C(0,3) = 10,000*0 + 3*20,000 = 60,000
C(1,2) =10,000*1 +2*20,000 = 50,000

Answer 5

I think I know what I would do... find coordinates for the corners of that shaded triangle, try each of those (x, y) values into the C equation and see which is smallest...
Yeah, kinda like that, I think. :)

Answer 6

I realize that I am not intimately familiar with this kind of problem, but I do know how to find regions with systems of inequalities and I don't believe that (0,3) and (1,2) are in that region. My vertices were (1,5), (4,2), and (28/19, 50/19). The wierd one was, of course, the minimum... at C=67,368.42105. Ignore me if you got it all figured out.

Answer 7

@EulerGroupie No i think your right

Answer 8

Cool, do you have what you need... or do you have any questions?

Answer 9

@EulerGroupie yeah im pretty sure! Thank you!(:

Answer 10

You're welcome.