An algebra word problem

Question

a fenced in rectangular garden is divided into 2 areas by a fence running parallel to one side of the rectangle. Find the dimensions of the garden that minimizes the amount of fencing needed if the garden is to have an area of 15,000 ft sq.

Answer 1

 

  Perimeter P = 2L + 3w

 

 Area = L*w = 15000 ----> L = 15000/w

 

  P = 2(15000/w) + 3w =   (30000 + 3w^2)/w

 

 

 The min occurs at w=100 where the perimeter is 600 and the length is 150

 per the graph using www.desmos.com

 

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calculus fans read on..........

 

 

 

 

 

 

 

 

 

Calculating the derivative, quotient rule says:

 

 [w(6w) - (30000 + 3w^2)]/w^2

 

 [ 6w^2 - 30000 - 3w^2]/w^2 =

 

  (3w^2 - 30000)/w^2

 

Setting equal to zero, the denominator vanishes....

 3w^2 - 30000 = 0

 3w^2 = 30000

  w^2 = 10000

  w = 100