00:01
Hello students in this question given maximize z is equal to 3x1 plus 8x2 subject to 3x1 plus 9x2 is greater than or equal to 27 and 2x1 plus x2 is less than or equal to 18 and x1 x2 are greater than or equal to 0.
00:30
So now let us convert this constraint into equation so 3x1 plus 9x2 is equal to 0.
00:38
So put x1 is equal to 0 sorry 3x1 plus 9x2 is equal to 27.
00:48
So put x1 is equal to 0 so we have 9x2 is equal to 27 that means x2 is equal to 3 and next putting x2 is equal to 0 so 3x1 plus 0 is equal to 27 so x1 is equal to 9.
01:11
So here we have the points 9, 3 and next we need to select the second constraint 2x1 plus x2 is equal to 18 putting x1 is equal to 0 x2 is equal to 18 and next x2 is equal to 0 so here x1 is equal to 9 so the points are 9, 18.
01:46
So now we need to sketch the graph so this is the graph so here we have two coordinate points they are 9, 3 and 9, 18.
01:58
So for the first equation 3x1 plus 9x2 or equal to 27 that means this area and 2x1 plus x2 is less than or equal to 18 that means this area so the common region is this one.
02:15
So now we need to find the extreme points so here extreme point coordinates x1, x2 lines throughout the extreme point and here let us write the objective function value...