# Mathematics

writing a report ，

The client for our project this quarter is Ryan Mack, founder of Nomad Joe. The purpose of this project is for each group to act as consultants for Nomad Joe, using calculus to advise on how to price a new product. The product Ryan is working to launch is a premium portable coﬀee kettle called the Voyager Kettle. In the labs you have developed a process for taking survey data, which gives the price potential customers would pay for a product, and using a linear regression to ﬁnd a model demand function for the price. In class, we have worked extensively to build a model which takes the price, estimates of the cost and the tools of extrema analysis and produces a suggestion for the optimal price at which to sell a product. At this point, I have asked your groups to collect and process the following: • Survey data about how much customers would pay for the kettle. • A linear regression of a demand function from your survey data. • A basic cost function including the base cost per unit and credit card fees. • A proﬁt function formed from your cost estimates and the revenue derived from your linear demand function.

In your last lab, your goal was to ﬁnish analysis on this model and obtain a recommendation on the price Ryan should set for his product. This means most groups are ready to start writing up their results to present to Ryan.

Presentation of Results

Each group has the option of either writing a report to present the results of their analysis and recommendations, or of giving a presentation in person to Ryan with an accompanying summary of results. In either case, your group’s job is to present your ﬁndings in as clear and convincing a manner as possible to our client. Written reports without an accompanying presentation should be around 3-4 pages long without the accompanying charts, graphs and ﬁgures you will want to include. Presentations should be 5-10 minutes long and should have an accompanying slide show or a brief written summary of results. Both written reports and presentations (either on the slides or in a summary) should provide the following information:

1. An introduction highlighting your most important results, namely the price recommendation.

2. An explanation of the method used to collect your survey, and a summary of the demand function obtained by regression. This should include the precise wording used in your survey. It is also a good time to discuss your thoughts on the target market.

3. An explanation of the cost estimates, particularly focusing on any terms your group has added beyond the basic cost per unit (i.e. marketing, etc.)

4. A brief description of the process used to form the proﬁt function and derive the maximum proﬁt. What kind of proﬁt do you think the Voyager Kettle can achieve under the demand you observed?

5. You must attempt to address at least one of the following additional questions: How will marketing eﬀect the costs and resulting maximum proﬁt? How can the demand curve for this product potentially be shifted to increase the maximum proﬁt? How can the statistics of the linear regression be potentially improved? How might your survey be adjusted to better ﬁt the target market?

6. An honest assessment of any problems with your model. What factors could have introduced inaccuracy into your results, and what could you do to improve? This is where you might discuss how marketing, or other strategies, might shift the current demand to something more favorable.

7. An appendix containing the following at minimum: Your raw survey data, a plot of your data along with the linear regression of the demand function, the mathematical details of deriving your cost, revenue and proﬁt functions and extrema analysis (i.e. a chart or table and your derivative analysis!) and a plot of the proﬁt function. All plots/graphs should be on appropriately scaled axes so the object of interest is in plain view.

Presentations should aim to be about 10 minutes long, and must include the appendix of data and calculations outlined above. Reports do not have a minimum page count, partly due to massive diﬀerences in each groups formatting of the report. However, a written report less than 3-4 pages long without its ﬁgures, tables and graphs would have a diﬃcult time addressing everything in the rubric well enough for top marks. Your reports and presentations will be shown to the client, so please prepare all materials with the client’s interest in mind. Make sure the information of interest, your recommendations, are featured prominently. Presentations should be clear and formal. It is recommended you use PowerPoint or some other visual presentation software. Reports should have a cover page, etc.

The client for our project this quarter is Ryan Mack, founder of Nomad Joe. The purpose of this project is for each group to act as consultants for Nomad Joe, using calculus to advise on how to price a new product. The product Ryan is working to launch is a premium portable coﬀee kettle called the Voyager Kettle. In the labs you have developed a process for taking survey data, which gives the price potential customers would pay for a product, and using a linear regression to ﬁnd a model demand function for the price. In class, we have worked extensively to build a model which takes the price, estimates of the cost and the tools of extrema analysis and produces a suggestion for the optimal price at which to sell a product. At this point, I have asked your groups to collect and process the following: • Survey data about how much customers would pay for the kettle. • A linear regression of a demand function from your survey data. • A basic cost function including the base cost per unit and credit card fees. • A proﬁt function formed from your cost estimates and the revenue derived from your linear demand function.In your last lab, your goal was to ﬁnish analysis on this model and obtain a recommendation on the price Ryan should set for his product. This means most groups are ready to start writing up their results to present to Ryan.Presentation of ResultsEach group has the option of either writing a report to present the results of their analysis and recommendations, or of giving a presentation in person to Ryan with an accompanying summary of results. In either case, your group’s job is to present your ﬁndings in as clear and convincing a manner as possible to our client. Written reports without an accompanying presentation should be around 3-4 pages long without the accompanying charts, graphs and ﬁgures you will want to include. Presentations should be 5-10 minutes long and should have an accompanying slide show or a brief written summary of results. Both written reports and presentations (either on the slides or in a summary) should provide the following information:1. An introduction highlighting your most important results, namely the price recommendation.2. An explanation of the method used to collect your survey, and a summary of the demand function obtained by regression. This should include the precise wording used in your survey. It is also a good time to discuss your thoughts on the target market.3. An explanation of the cost estimates, particularly focusing on any terms your group has added beyond the basic cost per unit (i.e. marketing, etc.)4. A brief description of the process used to form the proﬁt function and derive the maximum proﬁt. What kind of proﬁt do you think the Voyager Kettle can achieve under the demand you observed?5. You must attempt to address at least one of the following additional questions: How will marketing eﬀect the costs and resulting maximum proﬁt? How can the demand curve for this product potentially be shifted to increase the maximum proﬁt? How can the statistics of the linear regression be potentially improved? How might your survey be adjusted to better ﬁt the target market?6. An honest assessment of any problems with your model. What factors could have introduced inaccuracy into your results, and what could you do to improve? This is where you might discuss how marketing, or other strategies, might shift the current demand to something more favorable.7. An appendix containing the following at minimum: Your raw survey data, a plot of your data along with the linear regression of the demand function, the mathematical details of deriving your cost, revenue and proﬁt functions and extrema analysis (i.e. a chart or table and your derivative analysis!) and a plot of the proﬁt function. All plots/graphs should be on appropriately scaled axes so the object of interest is in plain view.Presentations should aim to be about 10 minutes long, and must include the appendix of data and calculations outlined above. Reports do not have a minimum page count, partly due to massive diﬀerences in each groups formatting of the report. However, a written report less than 3-4 pages long without its ﬁgures, tables and graphs would have a diﬃcult time addressing everything in the rubric well enough for top marks. Your reports and presentations will be shown to the client, so please prepare all materials with the client’s interest in mind. Make sure the information of interest, your recommendations, are featured prominently. Presentations should be clear and formal. It is recommended you use PowerPoint or some other visual presentation software. Reports should have a cover page, etc.The client for our project this quarter is Ryan Mack, founder of Nomad Joe. The purpose of this project is for each group to act as consultants for Nomad Joe, using calculus to advise on how to price a new product. The product Ryan is working to launch is a premium portable coﬀee kettle called the Voyager Kettle. In the labs you have developed a process for taking survey data, which gives the price potential customers would pay for a product, and using a linear regression to ﬁnd a model demand function for the price. In class, we have worked extensively to build a model which takes the price, estimates of the cost and the tools of extrema analysis and produces a suggestion for the optimal price at which to sell a product. At this point, I have asked your groups to collect and process the following: • Survey data about how much customers would pay for the kettle. • A linear regression of a demand function from your survey data. • A basic cost function including the base cost per unit and credit card fees. • A proﬁt function formed from your cost estimates and the revenue derived from your linear demand function.

In your last lab, your goal was to ﬁnish analysis on this model and obtain a recommendation on the price Ryan should set for his product. This means most groups are ready to start writing up their results to present to Ryan.

Presentation of Results

Each group has the option of either writing a report to present the results of their analysis and recommendations, or of giving a presentation in person to Ryan with an accompanying summary of results. In either case, your group’s job is to present your ﬁndings in as clear and convincing a manner as possible to our client. Written reports without an accompanying presentation should be around 3-4 pages long without the accompanying charts, graphs and ﬁgures you will want to include. Presentations should be 5-10 minutes long and should have an accompanying slide show or a brief written summary of results. Both written reports and presentations (either on the slides or in a summary) should provide the following information:

1. An introduction highlighting your most important results, namely the price recommendation.

2. An explanation of the method used to collect your survey, and a summary of the demand function obtained by regression. This should include the precise wording used in your survey. It is also a good time to discuss your thoughts on the target market.

3. An explanation of the cost estimates, particularly focusing on any terms your group has added beyond the basic cost per unit (i.e. marketing, etc.)

4. A brief description of the process used to form the proﬁt function and derive the maximum proﬁt. What kind of proﬁt do you think the Voyager Kettle can achieve under the demand you observed?

5. You must attempt to address at least one of the following additional questions: How will marketing eﬀect the costs and resulting maximum proﬁt? How can the demand curve for this product potentially be shifted to increase the maximum proﬁt? How can the statistics of the linear regression be potentially improved? How might your survey be adjusted to better ﬁt the target market?

6. An honest assessment of any problems with your model. What factors could have introduced inaccuracy into your results, and what could you do to improve? This is where you might discuss how marketing, or other strategies, might shift the current demand to something more favorable.

7. An appendix containing the following at minimum: Your raw survey data, a plot of your data along with the linear regression of the demand function, the mathematical details of deriving your cost, revenue and proﬁt functions and extrema analysis (i.e. a chart or table and your derivative analysis!) and a plot of the proﬁt function. All plots/graphs should be on appropriately scaled axes so the object of interest is in plain view.

Presentations should aim to be about 10 minutes long, and must include the appendix of data and calculations outlined above. Reports do not have a minimum page count, partly due to massive diﬀerences in each groups formatting of the report. However, a written report less than 3-4 pages long without its ﬁgures, tables and graphs would have a diﬃcult time addressing everything in the rubric well enough for top marks. Your reports and presentations will be shown to the client, so please prepare all materials with the client’s interest in mind. Make sure the information of interest, your recommendations, are featured prominently. Presentations should be clear and formal. It is recommended you use PowerPoint or some other visual presentation software. Reports should have a cover page, etc.5