A rectangular plot of land is to be fenced in using two kinds of fencing. Two opposite sides will use heavy-duty fencing selling for $5 a foot, while the remaining two sides will use standard fencing selling for $3 a foot. What are the dimensions of the rectangular plot that will minimize the cost of fencing to enclose 6000 square feet?

Question

anonymous · Answer

Area:  x y = 6,000
Perimeter: 
   P = 2 ( x + y ) 
Cost:
  C = 2 ( $3x + $5    y )
      =  2 (  3x  + 5 * 6,000/ x)
-> C' = ....
Minimize the cost happen when C' = 0   ==> x dimension  --> y

anonymous · Answer

so C' = 2(3-30000x^-2)
x=100?
y=60?

anonymous · Answer

Correct!

anonymous · Answer

ok thanks. that just helped me out a lot. i was confused b/c i had it equal to dC/dX