Homework 9 Solutions M331 Fall 2002
Average Score:
6.1. Let Nj be Neighborhood j (There are P of them, i.e. P = 1..j).
Let wij be the number of students going to school i from Nj Let rj be
the number of students residing in Nj Let ci be the capacity of school
i Let (xj , yj ) be the center of Nj Let (ai , bi ) be the location of school i
Then our program is:
min
S X
P
X
q
wij (ai − xj )2 + (bi − yj )2
i=1 j=1
such that
P
X
wij ≤ ci
j=1
S
X
wij = rj
i=1
√
6.2. Let f (x) = x2 − 3. Then the root of f (x) will be where x = 3
The iteration is
f (xn )
xn+1 = xn − 0
f (xn )
In our case, the iteration is
(xn )2 − 3
xn+1 = xn −
2xn
If you choose x0 = 3 then x1 = 2, x2 = 74 , x3 = 97
which converges to
56
√
3
6.3.
f (x) = 7x21 + 2x1 x2 + x22
∇f = (14x1 + 2x2 , 2x1 + 2x2 )T
14 2
Hf =
2 2
1