Consideration on Combinations of Postage Stamps

Quantitative Literacy, Level A Final Assessment: Outline and Rubric
Purpose of this Assessment
The purpose of the Final Assessment for this competency is to demonstrate successful use of quantitative reasoning appropriately within the context of a real-world situation.
Item Required for Submission
A 4-6 page paper in APA format with the four distinct sections detailed below for any of the investigations you select, following the guidelines for completing the paper completely.
Step ONE: Introduction (1 page)
Describe the investigation you selected. What is the problem about? What given information have you been provided? What kind of solution are you expecting? What else might be relevant to consider in your problem situation?
Step TWO: Using Mathematics (1 page)
Any plan for solving your problem should require using mathematics. What is the mathematics that is appropriate to use for your particular problem? What should be the plan for solving the problem using that mathematics? Are there different approaches for how to solve the problem? If so, why did you take the one you chose?
Final Assessment: Outline and Rubric 1
Quantitative Literacy, Level A Final Assessment: Outline and Rubric
Step THREE: Calculations (1-2 pages)
Effective communication requires organizing the calculations in such a way that the plan is evident. This would include the narrative discussing the calculations, as well as the calculations themselves. For readability, individual portions of this section can be placed in an Appendix if it is also organized and supports the plan by presenting it that way.
Step FOUR: Solution and Recommendations (1 page)
What solution did you find? How confident are you about the answer? If possible, how accurate is your answer, and how do you know? If there is another approach that could be used, would you get a better answer? Based on the work youve done, what recommendation are you making about the problem you described?
Step FIVE: Complete Checklist for Submission
Before you submit your work, check to see if you have met the criteria noted below. Did you: Make sure your introduction section contains the appropriate discussion for that section? Make sure your mathematics section contains the appropriate discussion for that section? Make sure your calculations section contains the appropriate discussion for that section? Make sure your solutions and recommendations section contains the appropriate discussion for that section? For readability sake, label any figure (table, graph, picture) with a brief description (e.g. Figure 3. Graph of Variable Relationship), and use the title in discussing it (e.g., Refer to Figure 3 and notice the positive slope exhibited) Demonstrate professional writing and presentation style by: your paper to ensure accurate spelling, grammar and punctuation? o Meeting the specified requirements of length and formatting specifications? o Providing citations using correct APA format if appropriate?
Step SIX: Submit Your Work Your completed files should be submitted through the Final Assessment page of your competency. Please note, for files smaller than 10MB (e.g., most Word documents), use the corresponding +UPLOAD STUDENT FILE button to upload your Final Assessment documents. For larger files of any type (e.g., voice over PowerPoint files, video presentations), please use the optional TEXT EDITOR to provide a URL where your tutorial faculty can download your file.
Final Assessment: Outline and Rubric 2
Quantitative Literacy, Level A Final Assessment: Outline and Rubric
How you create a download URL is up to you, but various free online providers, including Google Drive and Dropbox, offer this service. Please make sure that the URL you provide can be accessed by anyone with the link. For further instructions on how to create public links for uploaded files, consult the support pages for your chosen provider.
List of Templates/Resources Needed
APA 7th edition is required for your assignment. Review this comprehensive tutorial, which also contains a template that can be used for your assignment.
A Guide to Internalizing APA 7th Edition as a Style of Writing
Scoring Rubric for Final Assessment
Criterion EMERGING DEVELOPING PROFICIENT EXEMPLARY Introduction Not enough detail to understand the problem. No given information or no expected solution. The problem is discussed, maybe not enough detail, or some missing information or no expected solution. The problem is discussed sufficiently, including given information and expected solution. The problem is discussed completely, including all given information and expected solution. Mathematics Mathematics discussed is inappropriate for solving the problem with the current plan. Mathematics discussed is appropriate but not developed sufficiently to know whether the solution is achievable. Appropriate concrete mathematical structures (e.g., tables, graphs) are employed in planning the solution. Appropriate abstract mathematical structures (e.g. equations and geometric shapes) are employed in planning the solution. Calculations Calculations are sufficiently disorganized to the point that it impacts the readability of this section. Calculations are not organized. Three or more mistakes in calculations may be noticed. Calculations are organized and done correctly. One or two mistakes in calculations may be noticed. Calculations are organized and done correctly. No mistakes in calculations noticed.
Final Assessment: Outline and Rubric 3
Quantitative Literacy, Level A Final Assessment: Outline and Rubric
Solution/ Recommendati on
Solution may be not related to the calculations involved, or there is no analysis about the scope of the results.
Solution may be incomplete or somewhat fuzzy, or the analysis about the results is not developed completely.
Solution is explained and refers to the calculations. It provides appropriate analysis about the results.
Solution is clearly explained, refers to the calculations and provides appropriate analysis about the results.
Writing Mechanics
The paper lacks clarity and may be confusing; too long or short. Numerous errors in spelling, grammar and/or punctuation. No evidence of adherence to APA formatting.
The paper is somewhat logical and well-written; too long or short. Some errors in spelling, grammar and/or punctuation. Some deviation from APA formatting may be noticed.
The paper is logical, well-written, and the required length. There may be one or two minor errors in spelling, grammar and/or punctuation. APA formatting is followed.
The paper is logical, well-written, and the required length. Spelling, grammar and punctuation are accurate. APA formatting is followed.
Final Assessment: Outline and Rubric 4
Quantitative Literacy, Level A Final Assessment: Outline and Rubric
Appendix: Investigations for Summative Assessment
Investigation #1: Planning to Make Money
Some venture capitalists learned in economics that total revenue is the total receipts a seller receives from selling goods to buyers, and that it can be written as P Q, which is the price of goods times the quantity of goods sold. They hold the plans to the next hot technology gizmo that everyone will want to buy. In pricing the item, they made some assumptions:
1) For small quantities purchased, set the price low to invite people to get familiar with the product. 2) For large quantities purchased, set the price low as preferential treatment for your best customers. 3) Limit the number that can be purchased to a maximum of 1000 units. 4) An analyst recommends that the selling price for 500 units be $2500, or you will price yourself out of the market.
Therefore, they envision the pricing scheme shown in the graph as a rough model for projecting revenue. They have hired you as a consultant to make a recommendation about what the maximum revenue will be for the company under this business plan. Even though the units may be sold in different quantities, the central question to ask is, If all the purchases involved the same exact number of items, what would be the revenue for the company under that condition, and when would the revenue be as big as possible? This would provide a ceiling figure to report back to the investors.
Final Assessment: Outline and Rubric 5
Quantitative Literacy, Level A Final Assessment: Outline and Rubric
Investigation #2: Break-Even Point From Data
The Marketing Department has come up with the data shown in the graphs below. (Note: they are showing trends in the company performance.) You can see that the revenue peaks and starts to come back down, but the costs keep increasing, so the Management Team is concerned about when the company will break even.
Your job is to make a recommendation to the Management Team about approximately how far off in the future is the break-even point for the company. Without using statistical tools, model what the data indicates as a single cost equation and a single revenue equation. (If using specific points to model the equations, be sure to communicate what those coordinates are.) Then use your equations to find the break-even point and communicate your findings.
Final Assessment: Outline and Rubric 6
Quantitative Literacy, Level A Final Assessment: Outline and Rubric
Investigation #3: Time Series Analysis
In order to better understand the problem, an intern air traffic controller decides to simplify the problem of describing objects in motion. She decides to pretend the planes are flying along the ground at a constant height of 0 miles. Here is the simplified description of her problem, which uses Quadrant I of the standard coordinate system:
One plane has starting coordinates (0, 80). It moves in a westerly direction at 20 miles per hour and in a southerly direction of 10 mile per hour. Another plane has starting coordinates (200, 0). That plane moves in an easterly direction at 15 mile per hour and in a northerly direction of 30 miles per hour. A picture of the situation is shown below.
Will the planes collide? Why or why not? Explain how you would adjust the starting conditions of the problem in order to cause the collision to take place.
You may find the following tools helpful: time-series graphs show one directional motion over time, show horizontal and vertical motion without showing time (actual motion), and indicating the time at each point in a a time sequence state-space graph.
Final Assessment: Outline and Rubric 7
Quantitative Literacy, Level A Final Assessment: Outline and Rubric
Investigation #4: Comparing cell phone plans
LuckyUCalled is a company that offers several cellular service plans.
Based on your past history, you expect to use your phone anywhere between 100 and 300 minutes per month and it usually involves a data transfer of anywhere between 20 GB and 100 GB. If you restrict your attention to just these three plans that LuckyUCalled offers, which one would you select? Why?
Final Assessment: Outline and Rubric 8
Quantitative Literacy, Level A Final Assessment: Outline and Rubric
Investigation #5: Football Team Revenues
In basic terms, the total revenue from a professional football team should come from three sources: attendance at the live event, whether there is television revenue involved, and merchandising. It is reasonable to assume that:
attendance is related to the chance of success overall television exposure is related to the chance of success overall marketing can be related to the chance of success overall, but doesnt have to be. Star power can drive sales from outside your local fan base region
Here is some basic information about two professional football teams: the and the .
Los Angeles Rams Stadium capacity (70,240) Field level: 20,000 Loge Level: 25,000 Upper Level: 25,240 Ticket prices: Field level: $250/game Loge Level: $150/game Upper Level: $75/game Current COVID-19 restrictions: every 4th seat Television revenue: $40M per minute per game (60 minutes per game) Number of games per season to be televised: it could be 2 up to 8, based on chance of winning. Likelihood of a cancellation due to COVID-19: 40% Projected chances of winning 2022 Super Bowl (scale of 0 10): 7 Fan Base: 13,131,000 Merchandising History: when hot, sales of $100M; when not, sales of $10M
Tampa Bay Buccaneers Stadium capacity (65,890) Field Level: 25,000 Loge Level: 25,000 Upper Level: 20,890 Ticket prices: Field level: $200/game Loge Level: $100/game Upper Level: $50/game Current COVID-19 restrictions: every 5th seat Television revenue: $50M per minute per game (60 minutes per game) Number of games per season to be televised: it could be 4 up to 8, based on chance of winning. Likelihood of a cancellation due to COVID-19: 20% Projected chances of winning 2022 Super Bowl (scale of 0 10): 9 Fan Base: 4,000,000 Merchandising History: constant nationally at $50M due to the Brady phenomena
Compare these two cornerstone franchises of the National Football League. Based on this information alone, which team will make more revenue?
Final Assessment: Outline and Rubric 9
Quantitative Literacy, Level A Final Assessment: Outline and Rubric
Investigation #6: Comparing job offers
There are many factors to consider when comparing job offers the salary and benefits, the taxes, the cost of living, the cost of leaving, and other costs incurred by taking the new job. Here are three job offers for similar types of work for which you are eminently qualified. You currently hold the job in Silicon Valley, but you are considering choosing the offers elsewhere.
Location Silicon Valley, CA Seattle, WA Austin, TX
Salary Offer $250K $200K $150K
Retirement Benefits 8% contributed by employer
6% contributed by employer
7% contributed by employer
Other Benefits Stock option worth $200K
Tax Rate 13% 12% 7%
Cost of Living 60% above national average
40% above national average
20% above national average
Cost of Leaving Not vested yet. You lose 4 years of retirement accrued
To break the contract will cost $50,000 penalty.
Not vested yet. You lose the stock option.
Relocation Costs Up to $10,000 reimbursed
Up to 4% of salary Compensated an amount of $3000
You currently spend around $6000 per month in living expenses; you would live a similar lifestyle wherever you work. Project your total earning for five years into the future whether you stay put or take one of the other job offers. Which scenario provides the greatest accumulated earnings after five years?
Final Assessment: Outline and Rubric 10
Quantitative Literacy, Level A Final Assessment: Outline and Rubric
Investigation #7: Tile Counter Design
The classic Victorian tile pattern shown in the figure features green regular octagons and yellow squares in a tiling pattern that leaves no space between individual tile pieces. The pattern has been in such big demand that the manufacturer can no longer provide the green tiles to customers. The management thinks that it can design smaller pieces that can be fit together exactly to look like the original shapes, and the process can even be applied to the squares.
The management team has asked you to work on the problem, keeping the size of the pieces (number of sides) as small as possible. Imagine that you can manufacture as many pieces as you want, so supply will no longer be a problem. How many different shapes of each color would you want to start with? What would be their dimensions relative to the original tiling pattern?
Final Assessment: Outline and Rubric 11
Quantitative Literacy, Level A Final Assessment: Outline and Rubric
Investigation #8: Total Cost of a College Education
Think about when you were graduating from high school. If you knew everything you know now about going to college, would you still make the same decision? Specifically, what is the cost of getting a college education the total cost? Imagine a graduating senior who is wrestling with a similar problem — Should I go to college, or not? Analyze the situation using both your experience and what experts say about the problem. Then write a report to the student explaining the benefits as well as the costs of continuing with her/his education. Be sure to consider the total cost of getting an education the explicit and implicit costs involved. If you didnt go to college, you could get a job that pays $12/hour (if youre lucky). On the other hand, once you graduate, you can get a job that pays $40/hour to start. Consider all the lost revenue as well as the costs in your explanation.
Final Assessment: Outline and Rubric 12
Quantitative Literacy, Level A Final Assessment: Outline and Rubric
Investigation #9 Considering Combinations of Postage Stamps
Suppose you have 4-cent stamps and 9-cent stamps in unlimited quantities, and you can combine them to produce certain amounts of postage. For example, you can make 40 cents of postage by using four 9-cent stamps and one 4-cent stamp, or by using ten 4-cent stamps. However, there are some amounts of postage that you cannot make with those stamps, such as 10 cents.
What is the largest amount of postage that you cannot make exactly from a combination of 4- and 9-cent stamps? How do you know?
If you consider other types of stamps, are there combinations where you cannot answer the question, What is the largest amount of postage that you cannot make exactly from combinations of those types of stamps?
When you have done investigating this problem, you will be able to describe working with two generic types of stamps whose face values are a cents and b cents, and can tell the conditions under which the problem can and cannot be solved, and if it is possible to solve the problem, what the largest amount of postage that you cannot make exactly from combinations of those types of stamps. For example, if a = 4 and b = 9, then the problem can be solved and the largest amount of postage you cannot make would be 23 cents. But your description should output that answer from knowing the values for a and b.

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