00:01
Okay, so we want to maximize z equals 2x plus 3y, subject to the constraints that x plus y is less than or equal to 30, x is less than or equal to 20, y is less than or equal to 12, and x and y are greater than or equal to zero.
00:20
Now, part one says we need to convert this into a linear programming problem for each line.
00:24
Well, i think what this means is they want it in standard form, which means that you need to get rid of all these inequalities, other than the one that x and y should be greater than or equal to zero, and change them to equalities by introducing new parameters.
00:38
So if x plus y must be less than or equal to 30, then we can say that for some positive quantity, s1, x plus y plus s1 must equal 30.
00:51
Here, similarly, for some positive quantity, s2, x plus s2 equals 20.
00:59
And here for some quantity s3, y plus s3 equals 12.
01:05
And obviously, x and y are also greater than or equal to zero.
01:10
And then to solve this graphically, what we're going to do is just draw the graph.
01:16
So we've got x, the x -axis and the y -axis.
01:20
If we've got 12 here, and then six here, then we can sort of see that six, 12, 18, maybe 20, is here, and we know x has to be less than or equal to 20, and y has to be less than or equal to 12...