Maximize p = x + 8y subject to

P=? (X,Y)= ? (NOT BY GRAPHING)

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.

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).

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.

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.

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.

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)

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.

Find the series solution to the following differential equation:

y" + xy' - y = x^2 - 2x , about x = 1

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|

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?

Find the first 6 nonzero terms of the Taylor series solution to

y''=x+y^(3)-(y')^2 y(0)=2 y'(0)=-2

Given the following data, use exponential smoothing with a = 0.3 and α =.5 to develop a demand forecasts for period 7.  Assume that the forecast for week 1= 19. Use the Mean Absolute Percent Error to determine which forecasts are more accurate.

Agency – Practice Hypothetical’s

Basic Facts: Professor Green hires Helen Brown to sell his used law books for him because they are cluttering up his office. He says to her “you have authority to sell certain specified law books for $10.00 or more each.” Professor Green gives Helen the key to his office in order to show people the books and puts up signs all over campus which say:

USED BOOKS FOR SALE

Professor Green has Used Law Books for Sale

Price is Negotiable

See Helen Brown for further details

Professor Green also tells Helen the following:

1. Don’t sell, under any circumstances, my two books on agency law because I can never remember all the silly rules.

2. Don’t stand on the chair because it’s broken.

Hypo 1. Helen sells a corporate book for $25.00. Professor Green has forgotten to tell Helen that he also doesn’t want her to sell his contracts books. Can he get it back?

Hypo 2. Helen takes a second customer into the office and shows her the book selection. However, the dust on the books is so bad that the customer has an asthma attack and runs out. Helen hires someone to come in and clean the books and runs a bill of $25.00. Does Professor Green have to pay the bill?

Hypo 3. Helen takes a customer into the office and is offered $1,000.00 for the agency book. She is excited about the amount and, forgetting what Professor Green told her, sells it to the customer. Can Professor Green get it back?

Hypo 4. Helen sells Professor Green’s old corporations book for $5.00 and, getting angry, he demands that the customer return the book. Can he get it back?

Hypo 5. Helen steps on the chair to reach for a law book to sell it and injures herself. Can she recover any damages for her injury from Professor Green?

Mary has a limited food budget, but still wants to make sure her family members meet their daily nutritional requirements. Mary can buy two foods. Food 1 sells for $7 per pound, and each pound contains 3 units of vitamin A and 1 unit of vitamin C. Food 2 sells for $1 per pound, and each pound contains 1 unit of each vitamin. Each day, the family needs at least 12 units of vitamin A and 6 units of vitamin C. To minimize the total cost while satisfying the vitamin requirements, build a spreadsheet model to find out how much of each food Mary should buy. Answer the following questions (no need to present the model). (1) What is the optimal solution? (2) What is the minimum cost? (3) How is each vitamin requirement satisfied (exactly satisfied, or oversatisfied)?