00:01
All right, so we have a classic optimization problem with a rectangular fence.
00:05
So i'm going to go out this rectangle.
00:06
I know that i'm going to call my base x, my height, y.
00:10
So we're given that the area of this rectangle has to be 45 ,000 square feet.
00:15
So we know area of the rectangles, base time height, so we're just going to call this x, y.
00:20
So in this problem, no matter what dimensions the sides are, they must combine to give me an area of 45 ,000 square feet.
00:28
So that is kind of my restricting equation.
00:31
But what i'm trying to optimize here isn't the area.
00:34
The area is always going to be $45 ,000.
00:36
I'm trying to optimize the cost.
00:39
So i'm given some information about the costs.
00:42
For these two fences that are facing north and south, those are $4 per foot for the top and the bottom here.
00:52
Whereas the left and right fences, the ones facing east and west, those are $8 per foot.
00:58
So as i have these dimensions of x and y, how much is this going to cost me? so i'm going to write a new cost equation.
01:08
I'm going to call all at c for cost.
01:10
So i'm going to spend $4 per foot.
01:14
So this side is $4 times x feet.
01:17
So this is 4x and this is another 4x.
01:20
So i have two of these sides that are going to cost $4 per foot.
01:25
And i'm going to have two of these sides that cost $8.
01:28
Dollars per foot so that would be the cost of eight y so each one of these sides would cost eight y dollars so i can rewrite this this cost function is eight x plus 16 y so whatever the lengths of x and y are the cost would be eight x plus 16 y right because there's both the sides uh left and right right off the bat optimize this equation because it has both x's and y's so i need to come back over here use this restricting function to solve for one of these variables.
02:02
You could do either one.
02:03
I'm used to leave my equations in terms of x.
02:06
So we're going to go ahead and solve for y...