00:01
In the question it is given that, given that minimize, minimize c is equal to 2x plus y subject to, subject to x plus 2y is greater than or equal to 40, x plus y is greater than or equal to 30 and x comma y is greater than or equal to 0.
00:33
So, first we will draw the graph of constraints area defined by the four inequalities.
00:41
So, we have first x plus 2y is equal to 40.
00:48
So, from here x will be equal to 40 minus 2y.
00:52
We can see that if we have x is equal to 40, then we have y as 0 and if we have x is equal to 0, then we have y is equal to 20 and for the equation x plus y is equal to 30, we have x is equal to 30 minus y.
01:17
That means if we have x and y, x and y, if we have x is equal to 0, then we have y is equal to 30 and if we have x is equal to 30, then we have y is equal to 0.
01:33
Now, we will draw its graph and the graph will be like this.
01:37
This we have x axis and here we have y axis.
01:42
Now, if we withdraw, then for the equation x plus 2y is equal to 40 and if we have x is equal to 40, then we have y is equal to 0 and if we have x is equal to 0, then we have y is equal to 40.
01:56
So, we will join the line and we will get the line like this and for the equation x plus y is equal to 30, if we have x is equal to 0, then we have y is equal to 30 and if we have x is equal to 30, then we have y is equal to 0.
02:13
So, we will join the points and we will get the line like this.
02:18
So, this line is for x plus 2y is equal to 40 and this line is for x plus y is equal to 30.
02:29
So, we will have the required area here.
02:35
So, now when we draw the graph, then we get unbounded region.
02:44
So, the unbounded region is this.
02:46
Now, we need to find corner's point of this constraint region.
02:51
So, finding point b, we need to solve the equation, that is the equation we have x plus 2y is equal to 40 and we have x plus y is equal to 30.
03:04
Then we will subtract both the equation and we will get y is equal to 10...