00:01
Okay, for this problem, you're going to need to take a system of linear inequalities and plot them in order to come up with the solution region.
00:08
And then we've got to find the corner points and say whether it's bounded or unbounded.
00:12
And so we're going to start with our first inequality, which is x plus 2y is less than or equal to 10.
00:18
I'm going to use intercepts to find my, to plot, to find two points and plot it.
00:23
So i'm going to say first that x equals zero.
00:25
And i'm just going to make this into an equation because the inequality part only matters for the shading.
00:29
And so 2y is equal to 10.
00:33
So therefore, y would be equal to 5.
00:35
So this first point is 0 .5.
00:38
If y is equal to 0, well, that leaves us with simply x equals 10.
00:43
And so that would be 10, comma, 0.
00:46
So let's plot those two points, 05, which is right here.
00:51
10 .0 is right here.
00:55
We're going to connect that with a line.
00:59
It is a solid line because of the equal sign here.
01:02
And we know it's going to be shaded underneath it because it's less than, but we will deal with that in just a little bit.
01:11
So now let's do the next one.
01:12
We'll do a different color.
01:14
And we have 3x plus y, and it is less than or equal to 15.
01:23
Same strategy, x equals 0, leaves us with y equal to 15.
01:29
So that is going to be at 015.
01:33
And here we got y equal to zero, which is going to leave us with 3x equals 15.
01:39
And that's going to give me x equals 5.
01:43
And that's going to be 5 .0.
01:45
Okay, 5 .0 is right here...