Use induction to prove that 2 + 4 + 6 + ... + 2n = n2 + n for n ≥ 1.

Prove this theorem as it is given, i.e., don’t first simplify it algebraically to some other formula that you may recognize before starting the induction proof.

I'd appreciate if you could label the steps you take, Thank you!

In this assignment you’ll solve the basic economic order quantity (EOQ) model in Excel using two methods: (A) a trial-and-error approach to find a very good but approximate answer, and (B) the EOQ formula to find the “exact” answer. Set up your spreadsheet similar to that shown below.

The situation: Roxie is responsible for purchasing the paper used in all copiers and laser printers at Budco. After looking at her records, Roxie has found that demand for paper averages 600 boxes per month. The price of a box of paper is $20 (regardless of the number ordered). Placing and handling an order costs $66. Annual unit holding costs per box are 25% of the unit price. Last year, Roxie ordered paper once every two months, but she wants to know if another ordering policy would be cheaper.

1. Trial-and-Error (Approximate) Method

• Order Quantity: type in 25 for cell A10; then use the formula =25+A10 for cell A11 and copy this formula down, until Q reaches 1200.
• Annual Ordering Costs (DS/Q): for cell B10, use =$B$1*$B$3/A10; then copy formula down.
• Annual Holding Costs (HQ/2): for cell C10, use =$B$4*A10/2; then copy formula down.
• Annual Ordering + Holding Costs: for cell D10, use =B10+C10; then copy formula down.

Make a scatter (XY) chart of the Annual Ordering + Holding Costs (y-axis) vs. Order Quantity (x-axis).

2. EOQ (Exact) Formula

• Find the optimal order quantity Q* in cell E5 using the EOQ formula discussed in lecture and Ch. 12 of the text. You can find the square root of x in Excel with the function SQRT(x). In your E5 and F5 cell formulas you should reference other cells that contain the relevant data rather than typing the numbers themselves into the cell formula.

1. Based on the Trial-and-Error (Approximate) Method

A1. Approximately what order quantity minimizes total annual ordering + holding costs? ____ boxes

2. Based on the EOQ (Exact) Method

B1. What order quantity Q* minimizes total annual order + holding costs? _____ boxes

B2. What Excel cell formula is required for Annual Ordering + Holding Costs in cell F5? _____

B3. At Q*, what are the total annual ordering + holding costs? _____

B4. How many times per year will Roxie place an order of size Q*? _____

B5. Last year, Roxie ordered every 2 months. How much were her total annual ordering+holding costs?

_____________ (Hint: First ask yourself how many boxes would be ordered each time if you ordered exactly once every 2 months?)

B6. What is the percentage reduction in annual ordering + holding costs achieved by Roxie in following the optimalinventory policy instead of last year’s ordering policy? _______

Read the following case and answer the questions.

Greener Company

The CEO of Ferguson Inc. wants its executives to make the organization more environmentally friendly by encouraging employees to reduce waste in the workplace. Government legislation is coming that will require all companies of this size to have a program in place and the company’s customers also expect it. The CEO wants to significantly reduce paper usage, garbage and other waste throughout the company’s many widespread offices.

Unfortunately, a survey indicates that employees do not value environmental objectives and do not know how to “reduce, reuse, recycle.” As the executive responsible for this change, you have been asked to develop a strategy that might bring about meaningful behavioural change towards this environmental goal. What would you do?

Questions

1. Based on the case above, and according to Lewin’s Model for Managing Change - what are 2 Forces for the status quo (or restraining forces)?                          /2

2. Using Lewin’s Model for Managing Change, how would you go about implementing and managing the change at Ferguson Inc. – answer a. and b.                               

1. Explain each phase – Unfreezing, Moving and Refreezing  

2. and list one action that you would implement for each phase to accomplish your change.

What is the goals of Early vedic religion andn Late vedic religion?

Thank you!

Discuss key performance indicators in a business. Find some examples of key performance indicators and describe how they demonstrate the success of a company.

Have you ever read something that you suspected was fake news? In this week’s reading you will learn about strategies for determining if a source is credible. One of those strategies is the CRAAP Test.  

Currency: Is the information up to date?

Relevance: Is the information relevant to your research needs?

Authority: Who is the source of the information?

Accuracy: How reliable and truthful is the information? Can the information be verified?

Purpose: Why does the information exist?

How can the CRAAP Test help you when you look at news and articles in the future?

You have a program which has an interface for a remote

public interface Remote {
public void on();
public void off();
public void setChannel(int channel);
public int getChannel();
public void sleep(int numMinutes);
}

You've been working with a Spanish firm that wants to use your program, but they have a different interface

public interface controlRemoto {
public void enciende();
public void apague();
public void cambiaCanal(int channel);
public int qualCanal();
public void duerme(int numMinutes);
}

Create an adapter/wrapper around controlRemoto to make it look like Remote. For simplicity, the methods in both interfaces are in the correct order.

While working with the huffman encoding of n letters with frequencies g1, g2, g3, g4,....gn. Please state below the maximum length of a codeword possible. Please show proof to justify your answer.

Set T of integers is recursively defined as follows:

1. 1 is in set T

2. If x is in set T, then x + 2 and 2 ∙ x are both in T.

Which of these integers are in set T? 0 7 11 13 19 24

please explain why if possible, thank you!

The following algorithm multiplies two square matrices using a straightforward implementation of the definition of matrix multiplication.

(If you are unfamiliar with matrices, think of them as 2-dimensional arrays, and don’t worry, you don’t need to know how to do matrix multiplication to solve this problem)

1 2 3 4 5 6 7 8 9

10

ALGORITHM MatrixMultiplication(A[1..n, 1..n], B[1..n, 1..n])
// Multiply two square matrices of order n using the definition-based algorithm //Input: twon×nmatricesAandB
// Output: matrix C = AB
fori←1tondo

for j ← 1 to n do C[i, j] ← 0

for k ← 1 to n do

C[i, j] ← C[i, j] + (A[i, k] * B[k, j]) return C

The basic operations are the addition and multiplication of matrix elements at line 9. Determine the number of basic operations performed for two input matrices of size n × n. Write your answer in simplest form, if possible.

please try to explain how you did thi, thank you!

1a. What is the "one country, two systems" approach of China? How did it come about? How is the concept doing today?

1b. Describe and explain the four phases of the international planning process. Please provide example (s) when suitable.

1c. Describe the five characteristics of an innovation that assist in determining the rate of acceptance or resistance of the market to a product. Please provide examples.

1d. What has become the primary vehicle for doing business in many foreign countries? Explain and justify your answer with example(s).

1e. What are the various techniques that can be used to motivate middlemen? Please illustrate your answer with examples.