00:01
In this question we are given a linear problem that is we have to maximize z equal to 7 x1 plus 4 x2 plus x3 with the constraints that are subjected on z given as 2 x1 plus 2 x2 plus x3 less than equal to 18 x1 plus 3 x2 plus 3 x3 less than equal to 14 and x1 comma x2 comma x3 are greater than equal to 0.
00:39
We have to use the simplex method to solve this lpp.
00:43
So now we can write 2 x1 plus 2 x2 plus x3 we will add a slack variable s1 plus 0 s2 equal to 18.
01:00
So this equation then again second equation becomes x1 plus 3 x2 plus 3 x3 plus 0 s1 plus s2 is equal to 14.
01:18
So our z becomes 7 x1 plus 4 x2 plus x3 plus 0 s1 plus 0 s2.
01:29
Now we can form the table.
01:33
So cb xb the slack variables b the solution variables x1 x2 x3 and s1 s2.
01:46
Now cj values also we will write that is the coefficients of z that will be 7 4 1 0 0.
01:57
Now x1 x2 value for the two equations we will write 2 1 2 3 1 3 1 0 0 1.
02:10
So b values are 18 and 14 for both equations.
02:17
Two slack variables are s1 and s2.
02:21
So this will be 0 0.
02:24
Now we will find zj minus cj which will be equal to minus 7 minus 4 minus 1 0 0.
02:37
We will select the most negative value.
02:41
This is most negative value.
02:43
So x1 column becomes our pivot column.
02:47
Now we will find the ratio.
02:50
So we will divide 18 divided by 2 that is 9 and 14 divided by 1 that is 14...