00:01
We have a microbiologist that needs a solution, a medium, that is 13 % salt.
00:12
And given the constituents of the medium, or the nutrient solutions, are x, y, and z.
00:22
And the percent salt is given by 12x times y times z, and that needs to be 13.
00:28
So that's going to be our constraint equation, where that's not is 13 in this case.
00:32
Now, we're told that the solution, the nutrients cost $1 for x, $2 for y, and $3 for z.
00:42
So the total cost is going to be x plus 2y plus $3 .z and dollars.
00:47
So we want to minimize the cost given we need a solution, a medium with 13 % salt.
00:56
So our augmented function is g is ct, the cost, plus lambda, times s, our constraint.
01:03
We can a partial with respect to x, we get 1 plus 12 y z times lambda...