Project Title

Open for Business!



Have you ever wondered what it would be like to run your own business?† Business owners have to make decisions every day in order to maximize their profits (the money they make) and increase their number of customers.† If they price their product too low, they will have lots of customers but will make less money per product sold.† If they price their product too high, they will have fewer customers willing to pay the high price, but will make more money per unit.† Businesses are constantly researching and evaluating their pricing structure in order to stay competitive in the marketplace.



During the course of this project, your team will choose products to sell, conduct market research to set the prices, and evaluate the potential profits of a well-planned business.† First, you will choose two products that you would like to sell while keeping in mind your customer base (other students in your class or your school).† Next, you will need to research your cost in acquiring the products that you will sell.† After that, you will survey your classmates and group members to determine an acceptable price for your product.† Finally, you will write a mathematical model to represent your profit based upon the number of products sold.†



Solve each problem in order, keeping careful notes along the way.† From your notes, you will create a final presentation to share with your classmates.


1                     First problem:

                     What two products would your group like to sell?† Think about your customer base (your class).† What do students your age like to spend their extra money on?† You may want to take a survey of your class in order to gather more information.†


2                     Second problem:

                     What will the two products cost you to buy?† Research the prices online.† Determine your cost per unit based on your research.† Try the following websites for general merchandise, candy, or food products:


3                     Third problem:

                     Write and graph an inequality statement for the possible selling prices of each product.†† Graph the possible selling prices of each product on its own number line.††


(Hint:† Is there a minimum price for each product? How do you determine the minimum price? What is the maximum selling price?† It is okay to try a very high price for now.† You will collect data to set your reasonable price next.)


4††††††††† Fourth problem:

                     Make a function table to represent total profit as a function of the number of items sold.†† You should have four function tables, two for your first product and two for your second product.† One function table for each product should represent pricing your item at the minimum and the other will represent maximum pricing.†

                     Now graph the data for your first product on one coordinate plane and the data for your second product on another.† You should have two lines on each coordinate plane.


                     How are the two lines similar?† How are they different?† Calculate the slope of each of the four lines.† What does the slope of each line represent?† Notice that the area between the two lines represents the possible profits per item.† This profit will fluctuate based upon your choice in pricing.† You will look at determining an appropriate price next.†


5††††††††† Fifth problem:

                     Create a poll to test your selling prices.† Space your prices out between the minimum and maximum prices to determine what your classmates would be willing to pay for each of your two products.† You can conduct a poll in your classroom or set up an online poll using a site such as:




6††††††††† Sixth problem

                     Based on the results of the poll, determine your maximum reasonable price for each product.† Remember, if you set your prices too high, no one will choose to buy your products.† Be prepared to discuss how you chose this price during your presentation.


7 †††††††† Seventh problem

                     Determine your profit per unit for your first product, x.† For this project, your profit per unit will be the cost per unit subtracted from the selling price per unit.† Next, determine your profit per unit for your second product, y.† Your business will be considered successful if you can profit at least $100.† Using your profit per unit x, unit y, and the $100 goal, write and graph a linear inequality.† On your graph, x will be the number of units of your first product sold and y will be the number of units of your second product sold.† Use the model below to write your inequality.



(Hint for the graph:† Think back to standard form.† How many of only unit x would you have to sell to make your goal?† How many of only unit y?† There are also multiple combinations of x and y. How do you show this on your graph?)


                     Based on your graph, give three possible combinations of product x and product y sold in order to meet or exceed your goal.† Explain your reasoning for choosing each combination and mark each point that was chosen on your graph.†††




Determine the best way to share your project with your class.† You will need to share your solutions to each of the problems, as well as the necessary graphs.† You will also want to either have high quality pictures of your products or the actual products to show to the class.† Be sure to support each decision that you made with data from your class surveys or from your Internet research.† Your options for the presentation could include: a multimedia presentation, a project board, or an oral presentation.†



Discuss the benefits and drawbacks of the various types of businesses.† Take a class vote to determine which business would be the best to try to run within your school.† Is it possible to actually run your business before or after school?† Who would you need to contact for approval?† Consider giving your profits to charity or using them for a class party.††



Your project will be given a score of 1 to 4, with 4 being the highest score possible. You will be evaluated based on the following criteria:






Your project appropriately answers each of the problems, shows the steps taken, and the rationale behind each of your groupís decisions.


Your project appropriately uses single variable inequality statements and graphs to represent the possible prices of each product.† Your project also uses a two variable inequality statement and graph to represent the possible sales to meet the profit goal.

Your presentation contains information shown in a logical and interesting sequence that is easy to follow.


Professional looking visual aids add to the interest and help the audience connect with your presentation.†


Your project appropriately answers each of the problems and shows the steps necessary to solving each problem.


Your project uses single variable inequality statements and graphs to represent the possible prices of each product.† Your project also uses a two variable inequality statement and graph to represent the possible sales to meet the profit goal.† (A few minor errors in the inequalities may be present.)

Your presentation contains information presented in a logical sequence that is easy to follow.


Some visual aids are used to help promote interest in the presentation.


Your project minimally answers each problem, but does not show the steps taken to answer each problem.


An attempt is made to write and graph the necessary inequality statements, but major errors are noted.

Your presentation is hard to follow because the material is presented in a manner that jumps around between unconnected topics.


Some low quality visual aids are used but do not add interest to the presentation.


Some problems are unsolved and/or the steps taken to answer each problem are not shown.


Inequality statements and graphs are missing or inadequate.

Your presentation is difficult to understand because there is no sequence of information.


Visual aids are missing.

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