Josh wants to fence in 3 sides of his rectangular house with 1000 ft of fencing. The other side of the rectangular house would be a river. If the enclosed are is to be maximized,

a.) find the dimension of the house

b.) find the maximum enclosed area

Guest Dec 3, 2018

#1**+1 **

I think you want the dimensions of the fence

Let the two sides perpendicular to the river be = x

The side parallel to the river is then [ 1000 - 2x]

So, the area A is given by:

A = x [1000 - 2x] = -2x^2 + 1000x

The x value that maximizes this is = - (-1000) / [ 2 * -2] = 1000/4 = 250

So....the dimesions of the fence are 250 [1000 - 2*250] = 250 x 500

And the max area is 250 ft x 500 ft = 125000 ft^2

CPhill Dec 3, 2018