Question

PLEASE help? System of restraints?

Answer 1

I graphed it but I don't know what else to do

Answer 2

max/min values are the verticies of your polygon. in this case, you have 3 of them. try them all and see if they are max/min

Answer 3

@P0sitr0n I don't understand what I'm supposed to be 'trying', how do I find the max/min of the vertices?

Answer 4

you have some function that is determined by the constraints

the function can be evaluated above the plane along a new axis, and it forms a surface whose height form the plane is 3x+4y for a given point (x,y)

we have conditions set on x and y so that the valid points that can be used are form a restricted area in the plane, the triangle shale that you have shaded.

Answer 5

typos abound, but it should be readable

say we hold x at a constant value, and see how y affects the setup

x = 2, y ranges from 1 to 2

3(2) + 4y is greatest when y is at its max value

regardless of what x is along its interval, the max of the function is at the greatest y value along the region

Answer 6

we can plot some points along that slanted region

3(2) + 4(6) = 30
3(3) + 4(3) = 18
3(4) + 4(1) = 16

C is linear, its a line above the slanted portion that goes from 30 on the left, to 16 on the right ..... sooo, what this means is that we evaluate the corners of the region to determine the min/max of a linear constraint system

Answer 7

Okay, one moment, trying to understand all this @amistre64

Answer 8

@amistre64 So I make a triangle with points at 30, 18, and 16..?

Answer 9

the region that is bounded by the constraints define the domain of C

Answer 10

all points (x,y) in that region are valid for inputs into our C function

Answer 11

your region is defined by that shaded triangle, right?

Answer 12

Yes

Answer 13

then we need to determine a way to find the point in that region that gives us the maximum value.

Answer 14

do you know any calculus?

Answer 15

No

Answer 16

bummer lol

do you agree that if we evalute C for any point in that region, and map it as the distance above the plane, we get a surface?

Answer 17

Yes

Answer 18

the surface is linear, so its a plane, a sheet of paper above the region.

the corners of this sheet of paper are at these different heights above the plane

Answer 19

i cant draw it 3d ish ... but imagine holding a sheet of paper above the region so that its at those heights, what part of the paper is going to be farthest above the plane

Answer 20

Okay I'm starting to understand now, so are 30, 14, and 16 the maximum?

Answer 21

they are the critical points of interest, the rest of the points lie somewhere betwen the highest and lowest parts.

so all the points in the region are from 14 to 30 .....

Answer 22

whats our maximum ?

Answer 23

you graphed it, name the verts (2,2) (2,6) (4,1)

the verts define critical points of interest

what is the value of C at those points? which point is the maximum value?

Answer 24

Maximum is 30

Answer 25

@amistre64

Answer 26

correct, and for what value of x and y is that possible?

Answer 27

im logging out, the lag is unbearable ..

Answer 28

Okay, you've helped me a lot though, I think I can get the rest from here, thank you