00:01
So in this problem, we have this linear programming problem to do, where we have the max of z, trying to maximize z, defined as 60x plus 50y, subject to these constraints.
00:14
10x plus 20y is less than or equal to 200, 8x plus 5y is less than equal to 80, and x is greater than equal to 2, and y is greater than equal to 5.
00:28
And we're going to solve this graphically.
00:31
And when we do, we're going to give values for x, values for y, and then we'll calculate the z value and figure out which one is the max.
00:41
And then we'll be able to know what the optimal values are and which ones are slack.
00:46
Okay.
00:48
So let's go into our graphing calculator.
00:56
So i went to desmos .com, write down this graphing calculator.
00:59
So the first one, 10x plus 20y.
01:04
So i do 10x plus 20y is less than equal to 200.
01:24
There's that graph there.
01:28
Next one, 8x plus 5y less than equal to 80.
01:33
So we got 8x plus 5y plus 5y less than equal to 80.
01:41
Y less than or equal to 80 and there's that one we can see where they're overlapping now okay then we have x greater than equal to two so let's put that on here so i have x i don't need capital x any lowercase x greater than equal to two there everything to the right of that and then y is less than or equal to 5.
02:21
So here we'll have y less than equal to 5.
02:32
And we'll have all that down there.
02:34
And so what do we end up with? this means that we end up with these corner points, right? and the corner points are what's key here.
02:42
So we're here, here, and there.
02:51
Or the corner points, aren't we? okay.
02:57
So we have 2 .0, 25, 2 ,000.
03:02
0, 2, 5...