00:01
Hello everyone, in this problem we need to find the dimensions that will maximizes the area enclosed.
00:13
And it is also given that the farmer has 500 feet of fencing to work and those fencing are enclosed with two pens.
00:25
So now let us take the width of the pen to be l and l to be the length of the pen.
00:44
So now let us write the equation for total fencing which is available.
00:48
So it would be 2l plus 2x divided by 2 will be equal to 500 by upon simplifying and solving for l we have the value of l to be 250 minus x.
01:07
So now its area will be the product of the length and width that is l multiplied by x.
01:16
Now substituting the value of l to be 250 minus x so we get the area to be 250 minus x multiplied by x.
01:28
So now upon simplifying this we have this to be 250 x minus x square.
01:40
So now using vertex formula in finding the maximum value.
01:45
So let us take x to be equal to minus b by 2a...