Home Project Business Calculus Writing

Math 12: Take-home Exam Directions

This exam is due no later than THE END OF THE LAST CLASS MEETING IN
WEEK TEN. PAPERS SUBMITTED AFTER THIS DEADLINE WILL BE SUBJECT TO THE SLIDING PENALTY BELOW so make sure you have
something to submit on that day even if it is incomplete. If you cannot attend on the day the take home exam is due, you can email your take home exam to your
instructor as a SINGLE pdf file attachment no later than the end of the last class
meeting in Week #10. PLEASE DO NOT EMAIL INDIVIDUAL PAGES OF YOUR EXAM, SINCE I WILL NOT ACCEPT SUBMISSSIONS IN THIS FORM. I do NOT accept exams submitted to my campus mailbox. The time stamp on the email is used in establishing whether your exam is late.

Directions for writing up your final paper (Read carefully as your grade depends on your ability to follow these directions!)

1.    Put the date, your full name (as you registered in the class) in BLOCK letters at the top of the cover sheet of your paper (see last page of this document). Please staple all sheets together. Do not include any part of these question sheets in your solution.

2.    Your work should be neat and legible. If you can’t write legibly by hand, consider using a word processor and write in your formulas neatly by hand. Ink normally improves legibility. Do NOT use pencil anywhere in your paper.

3.    The paper should be self-contained; that is, the reader should not have to refer to any other document to see what your paper is about. This means you should introduce the topic at the start of your paper, and it should have a running narrative throughout till the end–including copying problem statements in each problem at the beginning, with your work following the problem statement.

4.    Answers without sufficient work will not earn full credit. Your work can be in the form of tables, graphs, equations, sentences in English, and even pictures. Consider highlighting or placing in a box, important numerical answers.

5.    If your paper is submitted late, a sliding penalty will apply. The penalties are as follows:

A)    Less than 72 hours (=3 days) late: a 50% penalty will be applied.
B)    More than 72 hours late: 100 % penalty (basically I do not accept work that is more than 72 hours (three days) late.

If you are unclear about ANY of the above directions, it is your responsibility to ask your instructor for clarification prior to the due date. It’s better to get things right the first time.

I will be happy to answer questions about the requirements for laying out your paper, but I do not offer help or hints with the mathematics. You are free to use any resources at your disposal.

Tips for writing good papers

I offer some strategies below to help maximize the points on your paper.

1.    When appropriate, make a clearly labeled sketch of the situation.
2.    Properly define your variables: e.g., let x be the amount of income earned.
3.    Do the problem on scratch paper first.
4.    Show ALL work (Don’t assume anything “obvious” or say to us, “I did it in my head”)
5.    Use correct mathematical notation throughout your paper. No short cut or “slang” uses of mathematics.
6.    When performing calculations, use all decimal places in your calculations until then end. Rounding of your final answer is permissible within reasonable limits.
7.    Use the equals sign (=) properly.
8.    Write in complete sentences.
9.    Assess the sensibility of your answer before you submit your paper. (e.g., Can
John really be 167 years old if John is a living human?)
10.    Show your write-up to a colleague and get their opinion on it BEFORE you submit your paper.
11.    Papers will not be returned to you. But you may view your graded papers by scheduling a mutually convenient meeting with your instructor. [I suggest you keep a copy of the original]
12.Though I encourage you to work with others in the class I frown upon direct copying from one student of another’s work. If I find evidence of this I will assign a zero score to ALL papers involved.

ADHERING TO GOOD WRITING HABITS

If you aim to get a perfect score your paper must be P E R F E C T! Here are some DOs and DON’Ts to bear in mind when writing up your paper. Good writing and clarity of intent is important if you want your mathematics to be understood by your reader.

The DO NOT list
Do not include any of the question sheets in your write up.
Do not submit illegible papers. If you are not comfortable writing by hand then word-process your document.
Do not submit tattered or paper with perforations such as that out of a spring binder.
Do not submit paper that is smaller than standard 11 x 8.5 inches or A4.  Do not submit unstapled sheets. (Asking your instructor for a stapler in class does not create the best impression of you.)
Do not submit graphs without labeling of axes and scales.

The DO list
Do explain your steps properly and completely.  If in doubt, write more rather than less.
Do connect mathematical expressions with short phrases in English.
Do pay attention to grammar and punctuation
Do write out your solutions using the same numbering as that which was used in the question paper; i.e. 1A, 1B, . . . 2A, 2B, . . . etc.
Do check your solutions via alternate methods when possible.
Do use graph paper and/or use software to make graphs. For example consider using this: https://www.desmos.com/calculator
Do make you paper self-contained. The reader should be able to understand the paper without having to refer to the original question paper. This includes writing an introduction to the topic of your paper.

Finally your document should look professional. If you would be embarrassed to submit it to an employer, then you should not submit it to your instructor.
Grading your paper

Based upon past papers, only a few papers are deemed “perfect” and receive a
5.

Perfect Paper
5 — (100%) —Exemplary response. Gives a complete response with a clear, coherent, unambiguous and elegant explanation; includes a clear and simplified diagram; communicates effectively to the identified audience; shows understanding of the problem’s mathematical ideas and processes; identifies all the important elements of the problem; may include examples and counterexamples; presents strong supporting arguments. Follows all directions for write-up.

Near perfect
4 — (90%) —Competent response. Gives a fairly complete response with reasonably clear explanations; may include an appropriate diagram; communicates effectively to the identified audience; shows understanding of the problem’s mathematical ideas and processes; identifies the most important elements of the problem; presents solid supporting arguments.

Satisfactory
3—(80%)—Minor Flaws But Satisfactory. Completes the problem satisfactorily, but the explanation may be muddled; argumentation may be incomplete; diagram may be inappropriate or unclear; understands the underlying mathematical ideas; uses mathematical ideas effectively.

Nearly Satisfactory
2—(70%)—Serious Flaws But Nearly Satisfactory. Begins the problem appropriately but may fail to complete or may omit significant parts of the problem; may fail to show full understanding of mathematical ideas and processes; may make major computational errors; may misuse or fail to use mathematical terms; response may reflect an inappropriate strategy for solving the problem.

Unsatisfactory
1—(40%)—Begins, But Fails to Complete Problem. Explanation is not understandable; diagram may be unclear; shows no understanding of the problem situation; may make major computational errors.

Failing
0—(0%)—Unable to Begin Effectively. Words do not reflect the problem; drawings misrepresent the problem situation; copies parts of the problem but without attempting a solution; fails to indicate which information is appropriate to the problem.

TAKE HOME EXAM

NOTE: The material from our text from Chapter 5 pertaining to optimizing functions will be helpful for this exam. Do NOT do work on this document nor include any part of it for your write-up, as explained in the instructions. Create your own exam document from scratch.

PART I: The Problem Statement
The Associated Students of Foothill College has decided to try publishing books as a way to make money for the college. A former professor of the college, Jane Erstwhile, has just written a new book, “Living in the Shadow of Jane Austen”. Ms. Erstwhile plans to sell an average of 100,000 books each month in the next year. You have been given the job of scheduling print runs to meet the anticipated demand while also minimizing total cost to the college. You have identified the following costs associated with printing the books:

A)    Setup Costs: Each print run costs $5,000
B)    Production Costs: Each book costs $1 to produce
C)    Storage Costs: Monthly storage costs for books awaiting shipment average 1¢ per book.

If you decide to print all 1,200,000 books (the total for the year, 100,000 books per month for 12 months) in a single run at the start of the year and sales run as predicted, then the number of books in stock would begin at 1,200,00 and decrease to zero by the end of the year, as shown in the graph below.

On average the college will be storing 600,00 books for 12 months at 1¢ per book giving a total storage cost of,

Storage Costs = 600,000 X 12 X 0.01 = $72,000

Recalling that the setup cost for the single print run is $5,000, the cost of producing 1,200,000 books at $1 each is $1,200,00, the total cost for the year would be given by,

C = (Setup Costs) + (Production Costs) + (Storage Costs)
=      $5000         +     $1,200,000     +      $72,000
= $1,277,000

EXAM QUESTIONS BEGIN HERE: BE SURE TO FOLLOW THE SAME NUMBERING BELOW IN YOUR EXAM WRITEUP.

1. You have an idea. To cut down on storage costs you will print the book in two print runs of 600,000 each, as shown in the figure below.

A)    What are the setup costs for two print runs?

B)    What are the production costs?

C)    What are the storage costs?

D)    What is the total cost for the year?

Remark
You should have gotten a total cost for the year of $1,246,000 for the year, resulting in a savings of $31,000 compared to the first scenario. Check your work above and fix any errors before you go on with this exam.
2. It appears to you that increasing the number of print runs reduces total costs for the year. Motivated by this idea, you decide to divide the 1,200,000 books into a twelve monthly production runs of 100,000 books each.

A)    Create a graph similar to the one in Problem #1 of this exam. Use graph paper and include the graph for your work in this part (You can glue the graph to your exam paper if necessary). Label both axes as in the graph above (you will have to modify the y-axis values for this part but should use the same x-scale).

B)    What are the setup costs for twelve (monthly) print runs?

C)    What are the production costs?

D)    What are the storage costs?

E)    Fill in the amounts from your work above and compute the total costs for the year:

C = (Setup Costs) + (Production Costs) + (Storage Costs)

Remark
You should have gotten a total yearly cost of more than $1,260,000 above, which is more than the total yearly costs for two print runs. So increasing the number of print runs to twelve has resulted in more total cost than for two print runs. So the question is, do minimum costs result with two print runs or can we do better?