# Economics/Statistics/Math

**Scenario: **For your next project, your boss asks you to research an application of linear equations in a business setting and present your findings to the team. **Do research using the Internet to find more information on 1 of the following topics**:

- Market Equilibrium
- Break-even analysis
- Inflation

**Part I: Primary Task Response**

In 3 paragraphs, report your findings to your classmates by discussing the following:

- Provide a general overview of the topic. There is no need to go deep into the math;
**simply explain what the topic means**in lay terms. - Identify at least
**2 ways the topic can be applied in business settings**. Explain. - Conclude your discussion by
**summarizing your key learning**from researching the topic.

Your company may wish to release a new e-reader device. Based on data collected from various sources, your company has come up with the following regression equation for the profit of the new e-reader:

Profit = $0.15 Ã— number of e-readers sold â€“ $28

Or, assuming *x* = the number of e-readers sold, this would be the same regression equation:

Profit = 0.15*x* â€“ 28

Answer the following questions based on the given regression equation:

- Using the graphing program that you downloaded, graph the profit equation. Discuss the meaning of the x- and y-axis values on the graph. (Hint: Be sure to label the axis)
- Discuss the meaning of the slope of the equation that you have just graphed. How is it related to the cost of each e-reader?
- Based on the results of the graph and the profit equation provided, discuss the relationship between profits and number of e-readers produced. (Hint: Consider the slope and y-intercept.)
- If the company does not sell a single e-reader, how much is lost ? Mathematically, what is this value called in the equation?
- If the company sells 5,000 e-readers, how much will the company make (or lose)?
- If profit must equal 100 thousand, how many e-readers will your company need to sell? (Round up to the nearest e-reader.)
- If your company is hoping to break even, how many e-readers will need to be sold to accomplish this? (Round up to the nearest e-reader.)Please submit your assignment

**Part I:**Most of the systems that we have discussed this week have been

**independent and consistent**systems. This means that the pair of lines intersects at one point so the system of equations has one solution. Do some research and discuss what is meant by a system that is EITHER

**inconsistent**or

**dependent.**Be sure to include in your response what each of these terms means in regards to graphs of the lines in addition to the behavior of the equations when you solve the system algebraically. Be sure to include the source that you used and to give an example of the system that you are describing.

a. How can equations and inequalities help a business maximize profit or minimize costs?

b. What is the importance of understanding how to set up and solve equations and inequalities (discuss in general without a mathematical example)?

This part of the assignment will contribute 20 points of the grade for this IP.

**Part III**

**Break-Even Analysis: A Look at Profit and Loss: **As an entrepreneur, there are going to be many decisions that you need to make, such as the price to charge your customers for your goods and services. You have just graduated from college and recently opened a specialty pizza restaurant. Based on surveys conducted in your area, you determine that it is feasible to sell your specialty pizzas for $15. The cost for making the pizzas includes a fixed cost of $55 and a labor cost of $4 per pizza.

a. Establish an equation to determine revenue.

b. Establish an equation to determine total cost.

c. How many pizzas must be sold to break even (i.e., you experience neither a profit nor a loss)? Interpret your result.

As a business owner, it is very important to have an understanding of profit and loss. The formula for determining profit is Profit = revenue â€“ cost (P = R â€“ C).

d. Determine the profit if 500 specialty pizzas are sold. Interpret your result.

e. How many specialty pizzas would need to be sold to make a profit of $1,100? Interpret your result.

f. How many specialty pizzas would you need to sell if you wanted to make a profit greater than $1,595? Interpret your result.

This part of the assignment will contribute 50 points of the grade for this IP.

**Mathematics of Finance**

**Part IV:** As an entrepreneur, there may be times when you must borrow money to fund the start of your business. You have just graduated from college, and your dream is to start your own business. Before you start your dream business, you need to research funding options.

Think of a business that you would like to own. Do research using the Internet to find more information about loans for small-business owners.

- Discuss how small-business loans work and your options for obtaining a loan.
- Discuss the process and procedures for obtaining the loan.
- Report your findings in 2 paragraphs.

This part of the assignment will contribute 20 points of the grade for this IP.

1. You find that a small business loan in the amount of 50,000 is the amount you need to purchase the restaurant location. After researching banks to find the best interest rate, you find that banks for small businesses offer the best interest rate of 9% interest that compounds monthly for 7 years.

a. What is the monthly payment for this loan?

b. Show the formula that you used and the values used for each variable to calculate the monthly payment.

c. What is the unpaid balance of the loan at the end of the 1st year?

d. Show the formula that you used and the values used for each variable to calculate the unpaid balance at the end of the 1st year.

e. What is the unpaid balance at the end of the 6th year? Show the formula that you used and the values used for each variable to calculate the unpaid balance at the end of the 6th year.

2. Diane works at a public university. She contributes $625 at the end of each month to her retirement fund. For the past 10 years, this fund has returned 3.84% a year, compounded monthly.

a. Assuming the 3.84% rate continues, how much will she have in her retirement account after 15 years?

b. Assume the economy has gotten better and that the fund now has a return of 7.72% compounded monthly. Since Dianeâ€™s salary has risen over the first 15 years, she can now contribute $1000 per month. At the end of the next 15 years, how much is her account worth?