Question

will fan and give medal.
given the system of constraints, name all the vertices of the feasible region. then find the maximum value of the given objective function.
constraints: x is greater or equal to 0
y is greater than or equal to 0
y is less than or equal to 1/3x+3
5 is greater than or equal to y+x

objective function: c=6x-4y

Answer 1

https://www.desmos.com/calculator/f5pg9wdie7
it's a link to the graph of the given constraints.

Answer 2

You should start by graphing the feasible region. You already have that. Next you should state the possible points that could result in obtaining the max value of the objective function. You already have the possible points.

Lastly, you simply test the points algebraically by plugging in each point into the objective function. So here are the steps:

1. Draw the graph of the feasible region
2. Express the possible points (the intersections of the given lines)
3. Test each point by plugging them in one at a time into the objective function
4. State the max value and the point that resulted in producing the max value.

Answer 3

https://www.desmos.com/calculator/eiacyfazay
sorry here is the right link

Answer 4

does that help

Answer 5

it kind of does, thank you! my only problem is i can't graph the answer i have to write it in numbers, do you have any idea on how to do that?

Answer 6

hold on let me check ok

Answer 7

thank you!

Answer 8

the maximum value

Answer 9

???

Answer 10

if you wanna know the truth i really dont know how to get to the maximum value either
i just tried but got lost in the process sorry i couldnt help with that
i tired my best

Answer 11

its fine! thank you for your help though :)

Answer 12

no problem
and thank you for the fan and medal

Answer 13

To find the Maximum and minimum values draw a line (with the same gradient as the objective function) at each corner of the feasible region, it must extend up to the y-axis. The point with the line that has the highest y-intercept is the maximum point and the point with the lowest y-intercept is the minimum point

Answer 14

@Renato19 should be correct

Answer 15

so i would draw a line from a point or? I'm confused.

Answer 16

Oh my goodness i am sorry! I have done it wrong! What are your vertices and what is your objective function?

Answer 17

hahah, its all good! :)
my vertices are (0,3) (0,0) (5,0) and (1.5, 3.5)
my objective function is c=6x-4y

Answer 18

Lol i had a brain fart here ill show how to get the max and min on a drawing

Answer 19

alright, thank you guys for taking your time to help!

Answer 20

You can draw a line at each vertice OR alternatively you can just substitute each point (x,y) into the objective function and the point that gives you the highest 'c' value is your maximum point and the maximum value is the c-value you get

Answer 21

now on this you solve and whatever is your lowest number is your minimum and your highest number is the maximum

Answer 22

Sorry its not the prettiest

Answer 23

Also the F should be C because of your equation has C=6x-4y

Answer 24

oh my! thank you both so much!! :) i understand hope to do it now!! i became a fan because i have already chose a best answer. so thank you all so much :)

Answer 25

Welcome! :) Im glad to have helped!