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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 

 Dec 3, 2018
 #1
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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

 

 

 

cool cool cool

 Dec 3, 2018

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