I S S U E 01 JA N U ARY 2023 Celebration of Lunar New Year SEL L ING ORANGES Delicious
Chuah Jia Ying (292050) Joan Ong Qi Jin (291928) Muhammad Aiman Zulhakim bin Mohd Zakilah (292042) A'IFIFAH AKHTAR BINTI MAZUKI (291920) GROUP MEMBERS:
Introduction 1 Methodology Scenario 1 Problem Solving 1 Scenario 2 Problem Solving 2 Conclusion TABLE OF CONTENTS 2-3 4 5-6 7 8-10 11
In Chinese culture, orange is a staple food during the Lunar New Year as a sign of luck and wealth. The Chinese culture has a longstanding custom of giving oranges as a gift accompanied by a red envelope containing money, which drives up the price of oranges on the market. Throughout the Lunar New Year celebration, the oranges are typically packaged in boxes by merchants and sellers to safeguard the oranges during transit and to preserve their freshness for the buyers. As a result, we will be measuring the ideal box size for carrying oranges and evaluating the Business & Economic (B&E) functions in this report. INTRODUCTION 1
This report's methodology section seeks to provide a basic overview of the methods and procedures utilised to collect information and data on the topic of measuring box dimensions to accommodate oranges and selling them oranges during the Lunar New Year. According to a qualitative research design, this report employed only qualitative data gathering and analysis tools and relied solely on research papers as its primary source of information and data. The box measurement and calculations for the following economic and business (B&E) findings were gathered and reviewed using the research study or reference approach. The study was completed with a primary focus on reading academic publications and conducting internet research as primary sources of knowledge of the box measurement and calculations for the following economic and business (B&E) findings. Internet research was conducted using various websites and academic resources to acquire relevant information and studies on the issue. Academic literature, including books and journals, was reviewed to better understand the topic. These sources were carefully selected and evaluated to ensure the information's authenticity and validity. METHODOLOGY 2
METHODOLOGY The following data analysis methods were employed in this research to assess and interpret the information gathered. (1) Content Analysis In the case of the report, content analysis was used to evaluate and analyse academic literature on differentiation. As an example, Asano (2012)’s book “An Introduction to Mathematics for Economics” thoroughly explains the differential calculus involvement in B&E, such as profit functional, maximum profit, and maximum revenue. A full explanation of those differential calculus calculations can be found in “Applications of Differentiation: Optimising Revenue”. [Video], (Ainan, 2019) (2) Thematic Analysis In order to identify themes and patterns in qualitative data, thematic analysis is used. Thematic analysis was used in the report to identify reoccurring themes in academic literature and online research on differentiation. These are the recurring themes from the academic literature and online research used in the report. (a) Mathematical properties of differentiation. Both Asano (2012)’s book “An Introduction to Mathematics for Economics” and “Calculus for Business, Economics and The Social and Life Sciences” (Hoffmann et al., 2012) provide similar comprehensive explanations of the mathematical properties of differentiation, including functions used in finding maximum revenue or rules used in finding the dimensions of a box such as product rule. 3
SCENARIO 1: Oranges are in high demand throughout the Lunar New Year for consumption and as presents. It is critical to sell oranges before the event to accommodate this demand. The key to ensuring that the oranges reach clients in good condition is to utilise boxes with 18-2x and x centimetres dimensions. Measuring the boxes' dimensions is necessary to determine how many boxes with the maximum volume are required to meet the increased demand for oranges during the Lunar New Year. Knowing the maximum volume of each box will help us optimise our inventory and guarantee we have enough boxes to satisfy demand. 4
18-2x 18-2 x x x 18-2x 18-2x Let x cm denote the length of the clipped portion of the square, To determine the maximum number of squares that must be removed, 1. First, let be the volume of box, Formula volume, V = l x w x h 5
After that, using the 2nd derivative test to maximize volume of box, The maximum value of V(x) is achieved when x = 3. So, in order to attain the maximum capacity of the box, we must trim 3cm from the square's side. Next, using the 1st derivative test to find the possibilities of x, Finding V'(x) is by using product rule, V'(x) = vu' + uv' 6
SCENARIO 2: Finding the profit functional, maximum profit, and maximum revenue are essential for maximizing orange sales returns. 7
According to market study, when the price per unit is RM, buyers will purchase x oranges, Producing the x oranges will cost RM, How much revenue, R(x) and profit, P(x) are obtained from producing x oranges, The revenue is the price, p(x) times the number of x oranges, is RM, The profit functional, is RM, 2. To find the profit functional, the maximum profit, and the maximum revenue. Formula profit function, P(x) = R(x) - C(x) Profit functional, P(x), 8
Using the 1st derivative test to find the possibility of boxes that can be sell, x, Next, using the 2nd derivative test to know the maximum profit, P(x) is maximum at x = 6 Therefore, 6 boxes of orange need to be sold in order to get maximum profit of RM76 Maximum profit, 9
Maximum revenue, Maximum revenue is at x = 100 (100, 1500) is maximum point. Therefore, the maximum revenue is RM1500 when 100 boxes of oranges produced. First, using the 1st derivative test to find the possibility of x, Next, using the 2nd derivative test to know the maximum revenue, 10
In conclusion, the Business and Economic (B&E) scenario focuses on activities related to the marketing of a particular commodity, including identifying the profit functional, maximum profit, and maximum revenue. To evaluate data, we take the oranges from the Lunar New Year celebration as an example. In scenario 1, we need to determine how many boxes with the maximum volume are required to meet the increased demand for oranges during Lunar New Year. Finally, we found that the maximum volume of the box is 3cm. In scenario 2, we need to find the profit functional, maximum profit, and maximum revenue. Finally, the profit functional is P(x)= -2.25 +27x -5. The maximum profit of RM78 is to sell 6 boxes of oranges. The maximum revenue is RM500 when 100 boxes of oranges are produced. CONCLUSION 11
REFERENCES ILial, M. L., Greenwell, R. N., & Ritchey, N. P. (2012). Calculus with Applications. Pearson. Hoffmann, L., Bradley, G., Sobecki, D., & Price, M. (2012). Calculus for Business, Economics, and the Social and Life Sciences, Brief Version, Media Update (11th ed.). McGraw Hill. Asano, A. (2012). An Introduction to Mathematics for Economics. Cambridge University Press. Ainan, C. (2019, September 2). Applications of Differentiation: Optimising Revenue. [Video]. YouTube. https://www.youtube.com/watch? v=nCChdG5Y5Zc&feature=youtu.be Teachoo. (2021, April 15). Ex 6.5,17 - Chapter 6 Class 12 Application of Derivatives (Term 1). https://www.teachoo.com/4412/712/Ex-6.5--17---A-squarepiece-of-tin-of-side-18-cm-is-made-into/category/Ex-6.5/ i
STUDENT 1 (MUHAMMAD AIMAN ZULHAKIM BIN MOHD ZAKILAH, 292042) Firstly, I would like to thank my group members for attentive throughout the making of the magazine and giving full cooperation for the assignment. I learned a lot of new things by exchanging ideas with my group members and most importantly learned additional knowledge about Calculus. STUDENT 2 (CHUAH JIA YING, 292050) First, I'm very glad to be in a group with my team members. I learned many things from them. During the discussion, they suggest many different ideas to make the magazine very interesting. Finally, I am very grateful to my teammates for their cooperation to complete the assignment in time. Lastly, I hope we can get a good mark in our assignment. STUDENT 3 (A’IFIFAH AKHTAR BINTI MAZUKI, 291920) To start, I would like to thank my group members again, who are always helping me with the assignment and their cooperation in making the magazine. Besides that, while doing this assignment, I felt more prepared to answer the questions on this subject. To sum up, I hope my group will get a good mark on this assignment. STUDENT 4 (JOAN ONG QI JIN, 291928) First and foremost, our group consisted of four members. At the beginning, we did not know about each other. But at the end of the project, my feelings were grateful because I discovered my insufficiency. And also, I now have a better understanding of the differentiation of functions and have learned about many applications of function differentiation in a lot of fields of specialisation. Other than that, I am very happy for our group members' teamwork and progress on this assignment. REFLECTION (Individual Reflection) ii