## Differential Equations Maple Assignment. Nonlinear Equations

1. a. Use Maple to find a general solution to example 2 from our Section 3.2 Notes.b. Now solve the same DE for the given initial conditions.c. Create a phase portrait showing the two solutions for the given initial conditions.

2. a. Repeat the three parts above for the DE b. Assuming this models a population, what is the carrying capacity of this population?

3. a. Solve the DE  by hand (check your answer in the 10e solutions manual, section 3.2, number 3). Take a picture of your work and insert it in your Maple worksheet.b. Now use Maple to solve both generally and with the initial condition.c. Graph the particular solution in the DE’s field plot.d. Why/How does Maple’s solution differ (if it does at all) from the text’s solution?

Save your project as last name_first initial_Maple2 and upload to Canvas by October 23, 2019.**Be sure to make comments as you go through the problems, and answer any questions in the worksheet.

## False Proofs Project

There are many false proofs in mathematics. In addition to examples in our lectures, the following article is an MIT student project: 

Xing Yuan, Mathematical Fallacy Proofs

http://dspace.mit.edu/bitstream/handle/1721.1/100853/18-304-spring2006/contents/projects/fallacy_yuan.pdf

For this project, you need to

* Search the Internet to get more new false proofs different from those in our lectures and in Yuan’s paper.  

*Get at least four examples, one for a topic in algebra, trigonometry, geometry and calculus.  

* For each false proof, explain what cause the false proof, and how to correct it.  Include the webpages as reference where you find the false proofs.  

## Ordinary Differential Equation 2

In this mini project,you are expected to provide the following three required components:

(1)Problem Statement

(2) Background Information

(3)Required Work&Solution

The sections containing your problem statement and background information must be typed

using a font size of 12 in“Times New Roman”.Moreover the background information section

must contain“your own words”describing the method used in solving the given problem.

## Hospitality Revenue Management

Our hotel/company: Four seasons Hotel/ Toronto Downtown

Our 2 competitors: Shangri-la and Ritz-Carlton/ Toronto Downtown

Assignment:

The Revenue Manager’s job has become even more complex today with the increased use of the internet by consumers to search for vacation packages, hotel rooms and of course the best value in rates. This also requires the revenue team to ensure it’s rates are up to date based on supply and demand in the marketplace, forecasts, their hotel’s position in their competitive set, changing economic variables, marketplace conditions and what the competition is doing in response to all of this as well.

Introduction – 5 marks Why this revenue management analysis is important to the revenue management program of your chosen hotel. How you conducted your research and any limitations to your research that would affect the results.

Part 1 – The Research (35 marks)

1. Pick a hotel which is part of a hotel chain (your “selected hotel”) and two primary competitors (6 marks). This must be submitted in Week 9 for approval as well as being part of your report.

2. What is the competitive advantage for your “selected” hotel over its competitors. (2 marks)

3. Design a SWOT analysis (4 main points under each of S,W,O,T) for each of the 3 hotels above. (12 marks)

4. Check rates for each of the 3 hotels for a leisure customer traveling on: (15 marks)

· A weekend (Friday and Saturday night stay)

· 2 consecutive nights – weekdays (Dec. 2019)

· 2 consecutive nights during March 2019 (if applicable to the demand in your market. You need to determine when March break is for your market). Or another high demand period

*your leisure customer may be a family, group of students, a couple – your choice. It must be the same customer profile for each hotel. Ask for the best available rate.

· Rates must be checked at the same time for each hotel for comparison purposes. Record the date and time when you checked the rates. This should be reflected on your spreadsheet of results.

i.e. Rates were checked on Nov. 5th for a possible booking for the dates of November 25th and 26th.

· The rates should be checked in a minimum of the following FIVE distribution channels.

· Call hotel reservation number. This may be the hotel directly or the 800 number for a chain. Make sure you identify which one.

· Check the hotel website.

· Check Three (3applicable 3rd party booking sites (i.e. expedia, booking.com etc.)

· You will need to print a screen shot of each rate that you find on the internet for each time period.

· *Present your rate findings in a chart. Each date period that you check should have its own chart. Put Dates on one Axis and Channels of Distribution on the other Axis. See sample on blackboard.

Part 2 – Analysis (23 marks)

Based on the rates and SWOT analysis what do you think is your “selected hotel’s” revenue management strategy on each of the dates is in the marketplace. Support your analysis with your research and what you have learned about the marketplace on each of the dates. *Rates should be presented in a chart/spreadsheet that is easy to follow and compare. Written analysis should refer to specific details on the chart.

a) Considerations (5 marks)

· Find out if there are any major events in the marketplace during the selected time periods.

· Determine if any new competitors are entering or leaving the marketplace during the time periods.

· Identify high and low demand days for each of the 3 time periods from Part 1.

b) Discuss “your selected” hotel’s revenue management strategies? Do you think they have a strategy? Why or why not? (5 marks)

c) Offer recommendations for your “selected” hotel to improve their revenue management process and ensure they are optimizing their revenue. (5 marks)

d) Describe and assess the “service” you received at each hotel you called? Would it impact your decision to book there? Why or why not? (3 marks)

e) Describe and asses “your” hotel’s social media strategy as it relates to revenue management. Mobile marketing and booking strategy? (5 marks)

Conclusion: (7 marks)

Conclude your findings in this report, including analysis and recommendations. This is a summary of what you found, learned and what you think “your” hotel should do going forward to improve their results.

Overall Organization and Presentation of report – (10 marks)

Report should be professionally presented. It should include: a title page with course name and number, my name and all full student names and student numbers. Include a title for your report: ie. “Revenue Management report for ______(company)”. Professional pictures about your project may also be included.

## Analytical Reasoning Questions

Solve the following questions. Detailed explanation for each question is to be provided for every sub part of the question.Diagrams can be used to explain answers if necessary. Answers should be typed but not hand written. Solve each question and it’s sub part. There are just 11 questions but it looks lengthy as every time the question is repeated for every sub part based on same question. Question1 and it’s sub parts

Question 2 and it’s sub parts

Question 3 and it’s sub parts

a)

b)

c)

d)

Question 4 and it’s sub parts

a)

b)

c)

d)

e) Question 5 and it’s sub parts

a)

b) Options 1,2,3,4,5,6,7 batches

c) Question 6 and it’s sub parts

b)

c)

d)

e) Question 6 and it’s sub parts

a)

b)

c)

d)

e)

Question 7 and it’s sub parts a)

b)

c)

d)

e)

f)

Question 8 and it’s sub parts

same question but slight change in last part of question.

Question 9 and it’s sub parts

Question 10 and it’s sub parts a)

b) e)

Question 11 and it’s sub parts a)

b)

C)

d) Question 12 and it’s sub parts

a)

b)

c) Question 12 and it’s sub parts

a)

b) Question 13

a)

b)

c) Question 14

a)

b)

## Linear Equations

Tom has received a new job offer!

He is told that his starting salary will be \$75,000.00 per year.

He is also told that his salary will probably be \$81,000.00 in four years.

We will use this data to try to anticipate his future earnings in any given year.

Assume that
y = Toms salary amount in dollars
And
x = the number of years worked

Steps

1. Use the data given to find the rate of change, or the salary increase per year. (Hint:compute slope)

We are now going to use a line to model toms salary growth

2. Use the data givin and the slope value from step 1 to write the slope-intercept form of the line.

3. Based of your equation from step 2 what will Toms salary be in ten years?

## Sheet1

 Jan-16 Feb-16 Mar-16 Apr-16 May-16 Jun-16 Jul-16 Aug-16 Sep-16 Oct-16 Nov-16 Dec-16 YTD 2016 5,034,854 5,021,264 5,020,340 5,026,387 5,051,228 5,117,419 5,085,306 5,137,805 5,136,128 5,104,981 5,176,374 5,228,783 61,140,869 Jan-17 Feb-17 Mar-17 Apr-17 May-17 Jun-17 Jul-17 Aug-17 Sep-17 Oct-17 Nov-17 Dec-17 YTD 2017 5,189,412 5,179,841 5,137,306 5,156,209 5,152,183 5,193,299 5,181,548 5,218,870 5,242,896 5,304,190 5,345,338 5,356,650 62,657,742 Jan-18 Feb-18 Mar-18 Apr-18 May-18 Jun-18 Jul-18 Aug-18 Sep-18 Oct-18 Nov-18 Dec-18 YTD 2018 5,389,408.00 5,440,621.00 5,472,135.00 5,512,198.00 5,570,685.00 5,480,631.00 5,666,211.00 5,696,517.00 44,228,406.00 Jan-19 Feb-19 Mar-19 Apr-19 May-19 Jun-19 Jul-19 Aug-19 Sep-19 Oct-19 Nov-19 Dec-19 YTD 2019 0 What the the average minimuem by month from 2016-2018 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec YTD 0 What the the average highest by month from 2016-2018 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec YTD 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov