00:01
Hello everyone, in this problem we are given with the linear programming problem.
00:05
So, now we need to maximize the given value of z and we need to find the corresponding x and y values.
00:13
So, we have this objective function as z to be equal to 4x plus y and subject to the constraints x plus y which is less than or equal to 81, 3x plus y less than or equal to 117 and y greater than or equal to 28.
00:30
So, for all these given constraints we can consider that to be x plus y to be equal to 81, 3x plus y to be equal to 117 and y to be equal to 28.
00:44
So, now using all these values we can solve this problem by graphical method.
00:53
So, it would be.
00:54
So, this is the graph which represents the three given equations and here the shaded region is the feasible region and the corner points are a is of 0, 81, b is of 18, 63, c is of 29 .6 and 28 and d is of 0, 28.
01:28
So, now we need all these points to check the value of z.
01:35
So, now at a z will be substituting here function is given as 4x plus y substituting the value of x to be 0...