Question

formulate the following as a mixed-integer program

the set X\{x*} where X={x in Z^n. Ax<=b} and x* in X

Answer #1

Formulate the sudoku as an integer program
Formulate the sudoku X problem as an integer program
please show steps and explanation

Prove or disprove the following statements.
a) ∀a, b ∈ N, if ∃x, y ∈ Z and ∃k ∈ N such that ax + by = k,
then gcd(a, b) = k
b) ∀a, b ∈ Z, if 3 | (a 2 + b 2 ), then 3 | a and 3 | b.

when z=f(x,y), where tan(xyz)=x+y+z, find az/ax and az/ay

Consider the following mixed-integer linear program.
Max
3x1
+
4x2
s.t.
4x1
+
7x2
≤
28
8x1
+
5x2
≤
40
x1, x2
≥ and x1 integer
(c)
Find the optimal solution for the mixed-integer linear program.
(Round your answers to three decimal places, when necessary.)

Define the relation τ on Z by aτ b if and only if there exists x
∈ {1,4,16} such that
ax ≡ b (mod 63).
(a) Prove that τ is an equivalence relation.
(b) Prove that there exists an integer n with 1 ≤ n ≤ 62 such
that the equivalence class of n is{m ∈ Z | m ≡ n (mod 63)}.

Definition of Even: An integer n ∈ Z is even if there exists an
integer q ∈ Z such that n = 2q.
Definition of Odd: An integer n ∈ Z is odd if there exists an
integer q ∈ Z such that n = 2q + 1.
Use these definitions to prove the following:
Prove that zero is not odd. (Proof by contradiction)

Problem 11-1
(a)
Indicate whether the following linear program is an all-integer
linear program or a mixed-integer linear program.
Max
30x1 + 25x2
s.t.
3x1 + 1.5x2 ≤ 400
1.5x1 + 2x2 ≤ 250
1x1 + 1x2 ≤ 150
x1, x2 ≥ 0
and x2 integer
This is a mixed-integer linear program.
Write the LP Relaxation for the problem but do not attempt to
solve.
If required, round your answers to one decimal place.
Its LP Relaxation is
Max
x1...

consider the following functions where a and b are unspecific
constants f(x)=x^2+ax+b/x-1, is the line x=1 necessary a vertical
asymptote, explain

Let A = {x ∈ Z | x = 5a+2 for some integer a}, B = {x ∈ Z | x =
10b−3 for some integer b}. Prove or disprove the statements. 1. A ⊆
B 2. B ⊆ A

Prove that the ring Z[x]/(n), where n ∈ Z, is isomorphic to
Zn[x].

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