## Written Project

In the project you must type in complete sentences and use correct spelling and grammar. You will be graded on clarity of presentation as well as on mathematical precision.

### Prompt

Farmer Jill needs a new pen for her pet billy goats. She would like the pen to be rectangular and have an area of 50 square feet. Unfortunately for Farmer Jill, as the sun rises, the billy goats have developed the habit of running full speed at the sun; knocking the East side of the pen over. So, Farmer Jill has decided to make the East side of the pen out of stronger fencing that costs $40/ft while the other three sides will be made out of fencing that costs$15/ft. Since caring for the billy goats already requires a lot of time and money, Farmer Jill wants to spend as little as possible on this new pen. So she needs you to answer the following two questions:

1. What dimensions will minimize the cost of the pen?
2. How much will it cost her to build that pen?

### What to include in the Written Project

This written project is not to be discussed on Piazza or any other online forum. If you find yourself struggling, you may email either myself or Kaelin to discuss the steps. You are not to receive any other outside help without permission. Your final written project should consist of two pages.

Page 1 should have at the top a copy of the problem. On this page, you should then hand-write all the correct steps to explain and support your work. Mathematically, the problem at hand is an optimization problem. You should review the Chapter 7 lecture notes to see which steps to include. You can also check these steps for solving an optimization problem. Be sure you do not skip the calculus steps of finding critical numbers and testing them appropriately!

Page 2 should be in the form of a typed letter to Farmer Jill that answers her questions and explains how you know you've arrived at the correct solution. Use complete sentences, explaining both at a level to someone who understands calculus, and to a "lay person" what the solution should be. Keep in mind that since Farmer Jill can see Page 1, she knows what algebra steps you performed; these should not be detailed in your letter. Your letter to Farmer Jill should address why these steps give you the correct answer. For the formulas you can refer to your "Page 1" as an attachment. Letters that are especially creative or humorous are encouraged, as long as they are clearly written and the mathematics is accurate.

Your work will be graded on how well you show all relevant mathematical steps and how well you explain the answer in writing. Both the mathematics and the English should be clear.

### Submission Process

The submission process for the Written Project is as follows:

• Part 1: Compile a project that is a single .pdf file.
• Option 1 (lower-tech). Print out the problem. Handwrite all or part of your solution on the page (and subsequent pages if necessary). Print out the typed paragraphs of your letter and glue these on. Then scan your finished document into a single .pdf file.
• Option 2 (higher tech). Handwrite the formula parts and diagrams for your solution and scan them in. Electronically combine the .pdf file of your scanned solution and typed paragraphs of your letter into a single .pdf document.
Other procedures are possible. The file MUST include your legible solution (both the written mathematics and the formal letter) in a single .pdf file.
• Part 2: Online submission
• Individually, each student will upload an electronic pdf. version of their report to their own Canvas account. Here are the steps for doing this: