Using induction: Show that player 1 can always win a Nim game in which the number of heaps with an odd number of coins is odd.
In: Advanced Math
Use the branch and bound method to find the optimal solution to
the following integer programming problem: maximize 7x1 + 3x2
subject to: 2 x1 + x2 < 9 3 x1 + 2x2 <13 x1, x2 > 0; x1,
x2 integer
Instead of using EXCEL Solver to solve this problem directly as an
integer programming problem, use EXCEL Solver to solve the LP
problems at each branch, with the appropriate constraints added,
according to the branch and bound algorithm. Be sure to draw a node
and branch diagram to illustrate the procedure, showing the
branches that are fathomed, noninteger variables selected, and the
optimal solution
In: Advanced Math
In: Advanced Math
Maximize p = x + 8y subject to
x | + | y | ≤ | 25 |
y | ≥ | 10 | ||
2x | − | y | ≥ | 0 |
x ≥ 0, y ≥ 0. |
P=? (X,Y)= ? (NOT BY GRAPHING)
In: Advanced Math
WEB ANALYTICS
Write a review applying some of the concepts to the fashion industry. Offer an introduction and a summary, Conduct additional research and offer at least four additional references and citations. Offer references and at least one citation for every reference.
In: Advanced Math
For any Gaussian Integer z ∈ ℤ[i] with z = a+bi , define N(z) =a2 + b2. Using the division algorithm for the Gaussian Integers, we have show that there is at least one pair of Gaussian integers q and r such that w = qz + r with N(r) < N(z).
(a) Assuming z does not divide w, show that there are always two such pairs.
(b) Fine Gaussian integers z and w such that there are four pairs of q and r that satisfy the division algorithm with N(r) < N(z).
In: Advanced Math
Definition 1 (Topological space). Let X be a set. A collection O of subsets of X is called a topology on the set X if the following properties are satisfied:
(1) emptyset ∈ O and X ∈ O.
(2) For all A,B ∈ O, we have A∩B ∈ O (stability under intersection).
(3) For all index sets I, and for all collections {Ui}i∈I of elements of O (i.e., Ui ∈ O for all i ∈ I), we have U i∈I Ui ∈ O (stability under arbitrary unions). A set X equipped with a topology O is called a topological space and the sets in O are called open sets.
Exercise 1. Let X be a set. (1) Consider O_trivial = {emptyset,X}. Prove that O_trivial is a topology on X. (2) Consider O_discrete = P(X). Is O_discrete is a topology on X? Justify briefly your answer. Hint. You have to verify whether the collections O_trivial and O_discrete satisfy the three properties in Definition 1.
In: Advanced Math
Problem 4 (Sets defined inductively) [30 marks] Consider the set S of strings over the alphabet {a, b} defined inductively as follows: • Base case: the empty word λ and the word a belong to S • Inductive rule: if ω is a string of S then both ω b and ω b a belong to S as well. 1. Prove that if a string ω belongs to S, then ω does not have two or more consecutive a’s. 2. Prove that for any n ≥ 0, if ω is a string of length n over the alphabet {a, b} that does not have two or more consecutive a’s, then ω is a string of S.
In: Advanced Math
Find the break-even point for the revenue and cost. Draw your
own graph on a piece of paper.
Fixed cost = $22,000
Variables cost = $15 per item
Price = $23
The break-even point is at ________ items.
In: Advanced Math
Use the data in the following table to create a fraction nonconforming (p) chart. The column of np represents the number of non-conforming units. Is the process in control? (5 points)
Sample |
n |
np |
p |
1 |
100 |
7 |
0.07 |
2 |
100 |
10 |
0.10 |
3 |
100 |
12 |
0.12 |
4 |
100 |
4 |
0.04 |
5 |
100 |
9 |
0.09 |
6 |
100 |
11 |
0.11 |
7 |
100 |
10 |
0.10 |
8 |
100 |
18 |
0.18 |
9 |
100 |
13 |
0.13 |
10 |
100 |
21 |
0.21 |
Question 2
A bank's manager has videotaped 20 different teller transactions to observe the number of mistakes being made. Ten transactions had no mistakes, five had one mistake and five had two mistakes. Compute proper control limits at the 90% confidence level. Is the process in control? Show your work.
In: Advanced Math
Find the series solution to the following differential equation:
y" + xy' - y = x^2 - 2x , about x = 1
In: Advanced Math
Let x, y ∈ R. Prove the following:
(a) 0 < 1
(b) For all n ∈ N, if 0 < x < y, then x^n < y^n.
(c) |x · y| = |x| · |y|
In: Advanced Math
In: Advanced Math
use the approximate Half-Life formula for the case described below.discuss whether the formula is valid for the case described. poaching is causing a population of elephants to decline by 8% per year. (1) what is the half-life for the population? (2) there are 10,000 elephants today how many will remain in 40 years? (3) does the approximate Half-Life formula give a valid a proxima station in the case described. yes or no?
In: Advanced Math
Find the first 6 nonzero terms of the Taylor series solution to
y''=x+y^(3)-(y')^2 y(0)=2 y'(0)=-2
In: Advanced Math