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Working with decimals in corner point method?

Hi everyone, I'm new here so I hope I have this in the right category. Also, I'm terrible at math so if I'm doing something wrong could you please tell me what it is and point me in the right direction? So the question I must answer is this:

Attachment 23376

I've been using this video as a guide into how to answer corner point method questions but when I do the work I am left with these as answers, tell me if I've done them correctly:

Linear Programming - Example 2 - YouTube

1st constraint: 7x + 4y ≤ 53

I'm eliminating the x variable to solve y

7 (0) + 4y = 53

4y = 53

4y/4 = 53/4

**y= 13.25**

Now I'm eliminating the y variable to solve x

7x + 4y ≤ 53

7x + 4(0) = 53

7x = 53

7x/7 = 53/7

**x= 7.57142****8571428571**

2nd constraint:

2x + 7y ≥ 21

y:

2(0) + 7y = 21

7y = 21

7y/7 = 21/7

**y= 3**

x:

2x + 7(0) = 21

2x = 21

2x/2 = 21/2

**x= 10.5**

3rd constraint:

2x - 3y ≥ -18

y:

2(0) - 3y = -18

-3y = -18

-3y/-3 = -18/-3

**y= 6**

x:

2x - 3(0) = -18

2x = -18

2x/2 = -18/2

**x= -9**

Now my problem is if these answers are correct, what do I do with the decimal numbers **(13.25, 7.571428571428571, 10.5)**? They would be impossible to sketch out on graph paper. Also an additional note, how do I figure out the point of intersection of two lines? I understand how to do everything up to that, and after that but I'm stuck on what do do with the decimal numbers. Any help would be much appreciated.

Re: Working with decimals in corner point method?

Are you really required to use that many decimal places? It seems it would be simpler to write 53/7= 7 and 4/7 but graphing (13.25, 17.57) would be sufficient to determine which points are "feasible" or not.

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Re: Working with decimals in corner point method?

I really don't know, that's why I'm so confused. Because the decimals would make it so much more difficult to display on graphing paper so I figured there was a simpler way of writing it. I found this problem:

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and I get most of it. I'm thinking this is how I should go about solving my own equation because if I answered this equation like I'm trying to now I'd get 133.33 as an answer to y for the second constraint which would be difficult to graph but they've seemed to have converted 133.33 into 400/3 but I don't understand where 400/3 comes from, how they got that as an answer to y? Can someone explain it to me so that maybe I can apply it to my own problem?

Re: Working with decimals in corner point method?

Thanks for the help, I think I figured it out.