Question

Please help? Will fan and medal!!
Find the values of x and y that maximize the objective function P=3x+2y for the graph. What is the maximum value? Show all work.

Answer 1

@amistre64

Answer 2

@sleepyhead314

Answer 3

@silverr

Answer 4

Have you found the vertice points?

Answer 5

no

Answer 6

Well first step is to find the points where you have a vertex ( a corner)
then take those points in plug them into P

Answer 7

should I plug in (0, 8) (5, 4) and (9, 0)?

Answer 8

i see another point

Answer 9

(0,0)?

Answer 10

yes

Answer 11

so plug in 0, 0 to p? how?

Answer 12

that would just give me P=0.

Answer 13

yes now plug in your other points

Answer 14

P=8

Answer 15

which point gives you that?

Answer 16

no wait oops p=16 and (0, 8)

Answer 17

ok two more points to plug in
which ever P is the highest is your max which ever point gives you the max is where the max occurs
(0,0) is actually where your min occurs because P=0 will be the lowest P you get

Answer 18

P=3x+2y
15+8= 23=P

Answer 19

P=27

Answer 20

so there are my answers so (9,0) is my max?

Answer 21

so P=27 is your max and (9,0) is where your max occured

Answer 22

ohh, okay. thank you so much!!! I have one last question could you help me???

Answer 23

I can try to help.

Answer 24

What is the solution to the following system of equations? Show all work.

Answer 25

3x+2y+x=7
5x+5y+4z=3
3x+2y+3z=1

Answer 26

Ok so what we would must helpful is comparing the top and bottom equation because they are already have a lot of common terms

Answer 27

ok

Answer 28

3x+2y+z=7
5x+5y+4z=3
3x+2y+3z=1*

Answer 29

3x+2y+z=7
3x+2y+3z=1

Answer 30

Just subtract the bottom equation from the top equation

Answer 31

ok

Answer 32

-3x-2y?

Answer 33

hmm... when I take 3x away from 3x I get 0
and when I take 2y away from 2y I get 0

Answer 34

oh from top to bottom. sorry I was like what?

Answer 35

3x+2y+z=7
-(3x+2y+3x=1)
==========
0 +0-2z=6

Answer 36

oh okay

Answer 37

You could have done it the other away around

Answer 38

I'll just go with that. So now we just have -2z=6

Answer 39

so you can solve that for z right?

Answer 40

yeah give me a sec to do so

Answer 41

z=-3

Answer 42

ok so take one of the equations we played with with the equation we didn't play with and replace the z in both with -3
so for example choosing of one of the equations we just played with 3x+2y+z=7
and the other other equation we didn't play with 5x+5y+4z=3
Replace the z in both with -3
and you will have system of 2 equations with 2 variables now

Answer 43

so plug in -3 in those two right now
?

Answer 44

3x+2y-3=7
5x+5y+4(-3)=3 ; 5x+5y+-12=3

Answer 45

@myininaya

Answer 46

yes?

Answer 47

is that right?

Answer 48

yes

Answer 49

I mean is that all?

Answer 50

you need solve the system 3x+2y=10 , 5x+5y=15 for x and y

Answer 51

you already solved for z

Answer 52

Do I just do all that I already did for z?

Answer 53

I will make it a little easy for you divide both sides of 5x+5y=15 by 5 so x+y=3
You have the system
3x+2y=10
x+y=3

Answer 54

If you want to setup for elimination like we did before I suggest multiplying the last equation there by either -2 and -3 (but not both)

Answer 55

so would elimination be easier?

Answer 56

do you have a preference ?

Answer 57

no

Answer 58

what would require less work?

Answer 59

out of what ways?

Answer 60

Any way, I just need to find the answer, without having to use so many steps because I have to show every single step I do.

Answer 61

Ok well I will help you more once you have done what I asked.

Answer 62

find x and y?

Answer 63

We were looking at two equations
...I asked you to set it up for elimination by multiplying the last equation be either -2 or -3...

Answer 64

"I will make it a little easy for you divide both sides of 5x+5y=15 by 5 so x+y=3
You have the system
3x+2y=10
x+y=3"
"If you want to setup for elimination like we did before I suggest multiplying the last equation there by either -2 and -3 (but not both)"

Answer 65

oh ok 3x+2y=10
-2x+y=-6
?

Answer 66

-2(x+y)=-2(3)
-2x-2y=-6
now -2x+y=-6

Answer 67

-2x-2y=-6*

Answer 68

not*

Answer 69

ok much better

Answer 70

so now you can add those equations together

Answer 71

yeah sorry I caught that too

Answer 72

add?

Answer 73

3x+2y=10
+ -2x-2y=-6
---------------
x+0y=4

Answer 74

x=4?

Answer 75

YEAH YOU DID IT! x=4 and z=-3

Answer 76

the only one left is y

Answer 77

awesome!

Answer 78

so I plug those in and find y

Answer 79

which equation should I use? the one we didnt use this time?

Answer 80

or you could use that 3x+2y=10 given x=4
and just solve for y

Answer 81

you can use any of those three equations we started with

Answer 82

or 3x+2y=10
or x+y=3

Answer 83

ok so I am gonna use the last one

4+y=3

but wait where do I put z?

Answer 84

you do not have to put z in we actually already did that to get the equation x+y=3

Answer 85

oh ok

Answer 86

so just solve 4+y=3

Answer 87

y=-1?

Answer 88

(x,y,z)=(4,-1, and what was z)

Answer 89

I will let you scroll up

Answer 90

huh?

Answer 91

we found x,y,z

Answer 92

and i didn't feel like scrolling up to tell you what we found for z

Answer 93

i was leaving that to you

Answer 94

yeah z was -3

Answer 95

thank you @myininaya so thats all there is to it?