Question

Graph the system of constraints. Name all vertices. Then find the value of x and y that maximize or minimize the objective function. Find the maximum or minimum value
6<_x+y<_13
x>_3
y>_1
Maximum for P=4x+3y

Answer 1

@ybarrap

Answer 2

@jim_thompson5910

Answer 3

I'll graph the system for you. One sec

Answer 4

If you were to graph this system of inequalities, then you'd get what you see that is attached. The red points are the corner points or vertices of the feasible region

Answer 5

I used geogebra to graph this system

Answer 6

What you do from here is plug each point into the equation P=4x+3y

The largest value of P that you get will be your maximum

Answer 7

what are the vertices?

Answer 8

the red points shown on that graph

Answer 9

they are the corner points of the feasible region

Answer 10

one of them is (3,3) and I'm sure you can spot the rest

Answer 11

how do I know which one to put for x and y?

Answer 12

x is along the horizontal axis

y is along the vertical

Answer 13

example: the red point on the far right is (12,1) since x = 12, y = 1

Answer 14

what do I do after I get all the vertices/answers?
I got the maximum and minimum answers.

Answer 15

what results did you get

Answer 16

maximum is 51 and minimum is 21.

Answer 17

you nailed both of them

Answer 18

is that all I do?

Answer 19

it looks like it just wants the max though

Answer 20

but you now know how to find either one

Answer 21

Should I circle them both?

Answer 22

yep, that's all you do


graph the system

find the vertices

plug each one in

sort the results and pick out the max and/or min

Answer 23

It says "Maximum for P=4x+3y"

so it looks like it just wants the max