00:01
Hi, now we are going to solve the linear programming problem.
00:04
Maximize p is equal to 30x plus 40y subject to the constraints 2x plus y is less than or equal to 14 and x plus y is less than or equal to 9 and x plus 2y is less than or equal to 16.
00:27
Now i take 2x plus y is equal to 14 and i label this one as equation number 1 and x plus y is equal to 9 and i label this one as equation number 2.
00:39
X plus 2y is equal to 16 and i label this one as equation number 3.
00:45
Now in the first equation if i put x is equal to 0 then we get the value of y is equal to 14.
00:55
If i put y is equal to 0 then the value of x is 7.
01:00
So the points of the equation 1 is 0, 14 and 7, 0 and next in equation 2 if i put the value of x is equal to 0 then we get the value of y is equal to 9.
01:18
If i put y is equal to 0 then the value of x is equal to 9.
01:22
So the points of the line 2 are 0, 9 and 9, 0 and next in the equation 3 if i put the value of x is equal to 0 then we get the value of y is 8.
01:38
If i put y is equal to 0 then the value of x will be 16.
01:43
So the points of the line 3 are 0, 8 and 16, 0 and next we have to draw these three lines in the graph then we get this graph.
01:58
Now this is our feasible region.
02:12
So we have to find the intersection of line 2 and line 3 and the intersection of line 1 and line 2.
02:19
Now the equation 2 can be written as y is equal to 9 minus x then we have to substitute this value of y in equation 3 then we get x plus 2 times of 9 minus x is equal to 16.
02:37
From this we get the value of x is equal to 2 then the value of y is 7...