Imagine that you are planning to open a small clothing store that sells designer jeans. you are anxious to make your first sale, but as a person who has strong business sense, you know there are management tasks to deal with long before you greet your first customer. many of these tasks involve the financial health of the business. to better understand and plan for your financial future, it will be important for you to interpret different kinds of algebraic functions.

in this activity, you will graph revenue and cost curves for your small business and determine your break-even point, the point when revenue equals cost. you will also decide on an optimal commission to pay your sales employees, one that will give them incentive to sell jeans but not break the bank. finally, as acting manager, you will investigate several different loan options that will put money in your pocket and get your business off the ground.



directions and analysis
task 1: break-even point
business owners must clearly understand the concepts of revenue, expense, and profit. these simple business ideas act together to determine the financial success of a company.

look up the definitions of revenue, expense, and profit, and write them below. write a simple equation that relates the three concepts.

type your response here:

open the spreadsheet tool and click the break-even point tab. the worksheet shows profit (p( revenue(r( and costs(c(x)) as a function of units sold. throughout this activity, the word unit refers to one pair of designer jeans. according to the profit curve p(x) for the data shown, how many units must you sell before you begin to make a profit? in other words, at what point does the profit curve cross the $0-axis? make sure the cells for m, b, and d work out to m = $40, b = $8,000, and d = $125.

the break-even point of your small business is the point at which your revenues equal your costs. this means that the amount of money that you make is equal to the amount of money that you are spending. profit is zero at the break-even point. study the curves for revenue, r(x), and costs, c(x). based on the current data, how many units represent the break-even point of your business? how does the value compare with the value you found in part b? what are the values for r(x) and c(x) at the break-even point? assume m = $40, b = $8,000, and d = $125.

type your response here: