Created/Modified Fall 2017 

 

x=30 35 38 39

y=28 26 24 22

Business Calculus Project

In this project, you are to present all your results in a "business report" (imagine you are presenting these results to potential buyers, or investors).This report must be typed.The details of your calculus and algebra work that support your results are to be included at the end.This project is worth 100 points.

Online Jewelry Store

Consider yourself as a passionate jewelry maker for many years.You create unique handmade jewelry designs and make the jewelry yourself.Your friends have encouraged you to sell your jewelry to earn some money while you are a student and to gain business experience.

In order to minimize costs, you decide to sell your jewelry online.You create beautiful bracelets, rings and earrings.The mathematics involved include determining the price to sell the jewelry to maximize profit and the number of items you need to sell to maximize profit.In addition you will look at the implications to price and profit when the cost of making your jewelry increases.

The writing includes a discussion of the merits and considerations of having an online marketplace vs. a brick and mortar store.You will also discuss the steps to take for a successful online business.

Business Introduction and Discussion

Introduction -[5 points]

Give your jewelry store a name.Give your business report an appropriate title.Choose one jewelry item to sell for the first four months of your business.In your own words describe briefly the jewelry item you will be selling.

Discuss at least four considerations when selling in an online marketplace as compared to a brick and mortar store.Include reference(s) for online selling sites or articles you have read for this information.

Important Steps to Having a Successful Online Business - [5 points]

Discuss at least five factors for preparing for an online marketplace store.For example, consider goals that you may need to set, how potential customers will view your product, and customer service.

Data Analysis

Price - Demand Equation -[15 points]

For the first four months of your marketplace, you have experimented with selling your jewelry item at different prices.

MonthPrice (p)Number Sold (x)January$30February$36March$38April$40

Determine the functional relationship between the price per jewelry item and number of items sold.The number sold,x, is theindependentvariable, while the price per bracelet,p(x), is thedependentvariable.To do this you must perform a linear regression.This will give you a linear model of the price-demand function for the given data.

• Choose four prices fromhighest to lowestbetween $27 and $20 and complete the table above. Choose an appropriate technology to do the linear regression. What is the regression equation p(x) = ax +b ?
• Use appropriate technology to create a graph of the scatter plot and linear regression line on the same set of axes. Ensure that your graph has a title and that the axes are labeled.
• Interpret the slope and they-intercept of this linear model of the price-demand function.
• Determine the domain of the p(x) price-demand function. This will help with the graphs that you will need to prepare.

Determine Revenue Function - [5 points]

Determine the Revenue function.

Determine Profit Function - [5 points]

You have determined that your total monthly costs are: C(x) = 8x + 150.Now, determine the profit functionP(x).

Plot the Revenue, Cost and Profit Functions - [5 points]

Using appropriate technology, plot the Revenue, Cost and Profit functions on the same plot. Ensure that your graph has: a title, appropriate scale, labeled axes and a legend for the three curves.

Using Calculus to Determine Quantity & Price of Product to Maximize Profit - [20 points]

• Use Calculus to determine the number of items that must be sold to maximize profit.
• Use a Calculus test to verify that selling this number of items will result in maximum profit.
• Determine the maximum profit.
• Determine the price per item to maximize profit.

Implications of Change in Cost toQuantity and Price of Product to Maximize Profit - [25 points]

Your variable costs (costs per item) go up because the material price has increased by 19%.Originally the cost was:C(x) = 8x + 150.

• Determine the new cost function and define it asN(x).
• Determine the new Profit function.
• Using appropriate technology, plot the Revenue, new Cost and new Profit functions on a plot. Ensure that your graph has: a title, labeled axes and a legend for the three curves.
• Use Calculus to determine the number of items that must be sold to maximize profit.
• Determine the price per item to maximize profit.
• Determine the maximum profit.
• Did you pass on all the additional cost to your customers? Explain your answer.

Ideas for Expanding the Online Market Place Store - [5 points]

Discuss at least four ideas for expanding an online marketplace store such as your Jewelry store.

Technology Considerations -[5 points]

Discuss what technology you chose to use to find the linear regression equations and why.Discuss what technology you chose to create the graphs of your scatter plot, linear regression line, and profit function.For full credit, be sure to discuss what technology options you considered, the pros and cons of each, and what considerations or concerns led you to make the choices you made.

Professional Report - [5 points]

Check to see if your business report is professionally written with college level writing and formal language, as well as correct grammar and punctuation. Use appropriate headings. Include at least two references.