00:01
Hi, i'm david and i'm here to have you and see your question.
00:03
In the question here we have the optimization problem where we have the objective function be equal to the x plus y.
00:10
We have the constraint of the x plus 3y small equal to the 12 and the 3x plus y it will be smaller equal to the 12 and this will be the maximize problem.
00:27
And we have also the both x and y greater than zero so the first thing we need to do is we need to find the intersection between them so we want to find the x plus 3y equal to the 12 and the 3x plus y equal to the 12 to find the intersection between them here i will times the first one by 3 and it will result in the 3x plus 9y equal to the 36 and the same thing will be on the second one 3x plus y equal to the 12 the reason why do that because i can do the subjection now if we do it this one will go to the 0 and 9y minus y will be the 8 y equal to the 36 minus 12 equal to the 24 therefore the y will equal to the 24 over 8 and equal to the 3.
01:28
When get the y equal to the 3, we can find the x equal to we use the first equation y, x equal to the 12 minus 3 times y will be the 3.
01:39
And then we get 12 minus 9 equal to the 3.
01:45
And therefore we have the point here.
01:47
The first point will be the x y, it will equal to the 3 3.
01:52
And then we need to find the interruption for the x and y intercept as well...