minimizing the cost is the same as minimizing the fencing.
xy = 150
f = 2x+y = 2x + 150/x
df/dx = 2 - 150/x^2
df/dx=0 when x^2 = 75
So a pen of size √75 by 2√75 will use the least fencing.
Check: for a given perimeter, maximum area is when the fence is divided equally among lengths and widths. Since our total fence is 2√75 + 2√75 you can see that this is true.
Farmer KIKO wants to build a 150-square meter rectangular pigpen for his pigs. One wall of the
pen will be the existing barn for his pigs. The other three walls will be built from mesh (net)
fencing that cost $ 20/meter. Find the dimensions of the pigpen that will minimize Farmer KIKO’s
fencing cost.
1 answer