Question

Bob wants to create two pens. One pen if for a garden and it needs a heavy duty fence to keep out the critters. This heavy duty fence costs $15 per foot. The dog pen shares a side with the garden and has a lighter weight fence on the other three sides that costs $5 per foot. If each pen is to have an area of 504, find the values of x and y that would minimize the total cost of the fencing.

Answer 1

x y = 504
y = 504 / x
The total cost of fencing:
C ( x ) = 2 x * 15 + 2 y * 15 + 2 x* 5 + y * 5 =
= 30 x + 30 y + 10 x + 5 y = 40 x + 35 y = 40 x + 35 * 504 / x =
= 40 x + 17,640 / x
C` ( x ) = 40 - 17,640 / x²
40 - 17,640 / x² = 0
x² = 17,640 : 40
x² = 441
x = √441
x = 21 ft
y = 504 : 21
y = 24 ft