00:02
So for this calculus problem, we need to write the given linear program problem in standard form, and then we need to convert all inequalities to equations and introduce slack or surplus variables as needed.
00:17
So the original problem is a max 5a plus 5b, sorry, sb, looks like an s anyways, and that is subject to a less than 100, b less than 80, 2a plus 4b less than 400, and then a b greater than or equal to zero.
01:03
So step one, convert the inequalities to equations using slack and surplus variables.
01:11
Slack and then s prime is surplus.
01:15
So a plus s1 equals 100, adding, and that's adding slack variables, variable s1 to convert a is less than 100 to a plus s1 equals 100.
01:31
You have b plus s2 equals 80, and that's adding slack variable s2 to convert b less, excuse me, b less than 80 to b plus s2 equals 80.
01:47
And then we've got a plus 4b plus s3 equals 400, and that's adding slack variable s3 to convert 2a plus 4b is less than 400 to 2a plus 4b plus s3 equals 400.
02:10
Step two, to introduce non -negativity constraints for slack variables, that's s1, s2, s3 less than or equal to zero.
02:23
So the problem in standard form now is max z equals 5a plus 5b.
02:36
This is a 5, not an s.
02:39
Let's try to, we're going to try to make this as clear as possible.
02:44
Five.
02:46
Oh, see, even i'm, even i'm messing up now.
02:53
5a plus sb.
02:56
Confusing, right? i wish they used a different variable, but it is surplus.
03:01
And this is subject to a plus s1 equals 100.
03:09
B plus s2 equals 80.
03:16
2a plus 4b plus s3 equals 400.
03:26
And then a, b, s1, s2, s3 greater than or equal to zero.
03:38
So next, let's identify the extreme points.
03:42
Extreme points occur at the intersections of the equations when we set the slack variables to zero.
03:47
I'll show you what i mean.
03:49
Put a number three over here...