Group Project MATH&148

Group Project MATH&148

Summer 2019

Directions: 1. Your group will have two (2) or three (3) members. No deviations on the

membership will be allowed. 2. Your group will be working on the problems following these directions.

3. Finished projects are due e-mailed to the instructor (ssaxton@cascadia.edu) by August 16, 2019 at 11:00am. Be sure to list all group members in your project.

Projects submitted after 11:00am on August 16, 2019 will be considered late. Five (5) points will be subtracted from the total points earned for every 24-hour period (day)

late. Group Projects submitted after 11:00am on August 20, 2019 will not be accepted.

4. A neat and organized copy of the groups’ calculations must be uploaded to

the assignment in Canvas for each member of the group by 11:00am on August 16, 2019. Scan the work as a single pdf file. Canvas will only accept pdf files. Files

uploaded after 11:00am on August 16, 2019 will be considered late. Five (5) points will be subtracted from the total points earned for late files. Files submitted after

11:00am on August 20, 2019 will not be accepted. 5. Your project should be able to stand alone. All questions should be answered

fully within the project. Treat this project as a presentation to a board. Be creative! 6. Projects must be in Word, with Excel graphs imported into the Word

document, formatted to print. The instructor will print each page of the project as it is submitted. Care should be taken to turn in final drafts of the group’s work. Messy

and/or incomplete projects will result in a lower grade.

Learning Outcomes for this Project: ▪ Apply and create projects which integrate the use of calculus in problem

solving.

▪ Creatively use mathematical and other problem solving strategies to formulate models and to interpret results.

▪ Communicate understanding of mathematical topics. ▪ Translate and illustrate using graphs, words, tables, mathematical symbols

and formulas. ▪ Clearly express ideas to an audience.

▪ Work in groups while listening and contributing with respect and honesty.

Project Criteria: The project is worth a total of 50 points. I will use the following criteria to determine your grade.

▪ Clear, logical progression is evident throughout the presentation of the project.

▪ The graphs, calculations, and interpretations are correct. ▪ The presentation is typed, thoughtfully planned, well-organized, and complete

according to the main point(s) of the project. ▪ The directions for the project are followed.

Brownie Demand The Lots of Chocolate Bakery collected the data in the table below on the price of a dozen brownies, in dollars, and the number of dozens demanded per day.

Dozens Demanded

Price, in dollars

14 4.00

19 3.75

21 3.50

23 3.25

26 3.00

31 2.75

35 2.50

1. Find a price-demand function for the data where x is the number of dozens of brownies

demanded per day and 𝑝(𝑥) represents the price at which people buy exactly 𝑥 dozen brownies per day.

2. Graph the data and this equation using Excel. Import the Excel graph into your project. 3. Determine the revenue function, 𝑅(𝑥), as a function of 𝑥.

4. Determine the price that this bakery should charge to maximize the daily revenue.

5. If each dozen of brownies costs the bakery $1.50 to make, find the profit function, 𝑃(𝑥), as

a function of 𝑥. 6. Determine the price that this bakery should charge to maximize the daily profit.

7. The price-demand function for this data can also be modeled by

𝑝(𝑥) = 5.64𝑒−0.023𝑥, 14 ≤ 𝑥 ≤ 40 where 𝑥 is the number of dozens of brownies demanded per day and 𝑝(𝑥) represents the price at which people buy exactly 𝑥 dozen brownies per day. Complete steps two through six with this new price-demand function.

8. If you owned The Lots of Chocolate Bakery, which price-demand function (from part 1 or

part 7) would you use to determine the price of your brownies? Explain your answer using the information from the project.