00:01
So in this question they say i want to graph the feasible region that's identified by the inequalities.
00:07
4x plus y is less than or equal to 12, 2x plus 7y is less than or equal to 28, x is greater than or equal to 0, and y is greater than or equal to 0.
00:21
So first of all, if both x and y are greater than or equal to 0, that means i'm in the first quadrant since x equals 0 is just the y axis and y equals zero.
00:38
That's just the x axis.
00:42
So now thinking about 4x plus y is less than equal to 12.
00:48
This is a line and it would have an x intercept of 3 and it would have a y intercept of 12.
00:57
And so roughly speaking, here would be the line 4x plus y is equal to 12.
01:11
And so if 4x plus y is less than or equal to 12, we would be beneath that line in the first quadrant.
01:19
Now i also have 2x plus 7y is less than or equal to 28.
01:26
So intercepts here, i have an x intercept of 14.
01:30
Which is way out here, and i have a y intercept of 4, which is right here.
01:39
And so we're going to have something that looks like this.
01:45
So this guy here would be 2x plus 7y equals 28.
01:53
And so my feasible region, since 2x plus 7y is less than or equal to 28, lies beneath that as well, it's going to be this purple shaded region.
02:06
This purple shaded region that has its vertices at 0 ,0, 04, 3, and i do want to figure out what this intersection point is.
02:21
Now, to do that, i'm going to say if 4x plus y is equal to 12, that means that y itself is equal to 12 minus 4x.
02:31
Plug that into my second equation, giving me 2x plus 7 times the quantity of 12 minus 4x is equal to 28.
02:46
So 7 times 12 is 84.
02:50
7 times negative 4x, negative 28x, and all of this equaling 28.
02:59
So now combining my terms, i've got 2x minus 28x.
03:04
That's negative 26x...