00:01
Okay, and your question, we're trying to fence in an area that has a total area of 30 ,246 square feet.
00:15
We're told that we have an existing fence that we're building off of, basically.
00:20
So the pen that i'm trying to make is this region right here.
00:25
We're told that it's rectangular.
00:27
So i'm going to make this side x, which would make this side x.
00:32
And the length could be something different, so i need a different variable y.
00:37
Okay, so ultimately we're told that this y side of fencing costs $18 a foot, and the x fencing is costing $6 a foot.
00:57
All right, so what i want to do first is i want to create a function that stands for what i'm trying to minimize or optimize.
01:06
In this case, i'm trying to optimize my cost.
01:10
And my cost is going to be based on taking $18 times y plus, i'm going to make this, i could say $6 times x plus another $6 times x since we have two of those sides of our fencing, and we'll simplify that to 12x.
01:32
Okay, so what i have here is what i like to call my primary equation.
01:38
It's the equation that i'm trying to optimize.
01:41
Then i'm looking for any other information in the problem, say, and i call this a secondary equation.
01:48
And we know that x times y, x times y, should give us the area, and it needs to be 30 ,246.
02:00
Now, what we typically do with our secondary equation is we solve it for a variable.
02:06
I'm going to solve it for y.
02:07
So i have y equals 30 ,246 divided by x...