00:01
Here we're giving that a builder which is to have a rectangular structure around a piece of land and this will be 80 ,000 square meters and we'll call this x and the lengths will call them y.
00:25
Since they want to minimize the front of this land because they are going to use a lot more expensive type of fence.
00:38
So we will call this side the side in yellow the front and if that is the front therefore it will cost 60 x in fence and the rest of the side will cost 20 per meter so we are with 20 y.
01:12
Here we have 20x and there we have 20 y.
01:21
We chose the shorter side to be the front since we want to minimize the cost, the overall cost.
01:29
So here we have our cost function, our cost function c of x and y is equal to there we have 60x plus 20 y plus 20 y plus 20 x and we simplify that we have 80x plus 40 y is our expression of the cost function and the area is given by length by width which is x y and this is equal to 80 ,000 we'll call this equation one this one equation two now if we want to have our cost function just in terms of x so here our would have y is equal to 80 ,000 over x and plugging that into the first equation we have 80x plus 40 in terms of y instead of why we put 80 ,000 over x and and simplifying this we have 80x plus 40 by 80 ,000.
02:57
We get 3 ,200 ,000 over x over x.
03:10
Now this is our cost function.
03:11
Since we want to minimize, we need to find the critical values...