Question

Given the system of constraints, anem all the vertices of the feasible region. Then find the maximum value of the given objective function. Objective Function: C = 6x – 4y

Answer 1

your first need to graph the inequalities

Answer 2

okay that'll take me a few minutes

Answer 3

alright post what you get

Answer 4

ideally, using geogebra (not sure if I showed you that program or not) is the best way to do it

Answer 5

alright thats what i got so far

Answer 6

ok one sec

Answer 7

I think i made a mistake I think this is the right one

Answer 8

ok much better

Answer 9

that's a very messy picture, but all 4 graphs overlap to give you this

Answer 10

so are my points (0,0) (0,3)(0,5)(1.5,3.5)??

Answer 11

one sec, gotta check that last point

Answer 12

instead of (0,5), it should be (5,0)

Answer 13

everything else is correct

Answer 14

your four corner points are (0,0), (0,3), (5,0), (1.5,3.5)

Answer 15

do you know what to do from here?

Answer 16

yup give me one sec

Answer 17

ok tell me what you get

Answer 18

the max is the largest value of C that occurs when you plug in each corner point

Answer 19

so -20

Answer 20

if you plug in each corner point you get this

Answer 21

Plug in (x,y) = (0,0)


C = 6x - 4y


C = 6(0) - 4(0)


C = 0


---------------------------------------------

Plug in (x,y) = (0,3)


C = 6x - 4y


C = 6(0) - 4(3)


C = -12


---------------------------------------------

Plug in (x,y) = (5,0)


C = 6x - 4y


C = 6(5) - 4(0)


C = 30


---------------------------------------------

Plug in (x,y) = (1.5,3.5)


C = 6x - 4y


C = 6(1.5) - 4(3.5)


C = -5


---------------------------------------------

Summary:


Min is C = -12 which occurs at (0,3)


Max is C = 30 which occurs at (5,0)

Answer 22

oh sorry I had 0,5 written down that makes more sense

Answer 23

ok great

Answer 24

Thank you for all your help!

Answer 25

yw