# Bagels or Donuts - A Balanced Assessment Task

- Author:
- Judah L Schwartz

Your school has offered you an opportunity to run a breakfast concession in the cafeteria. You will be allowed to sell either bagels or donuts, but not both. Your market research indicates that students are indiscriminate consumers of toroidal breakfast food: they would buy the same quantity of either product at your planned selling price. Therefore your choice of which item to sell will depend upon which you can obtain at a lower cost.
Your bagel supplier requires that you make an initial payment to cover franchise fees and delivery costs for the rest of the school year {use the GREEN dot to choose an amount in $ for the fixed cost of doing business – for example, anywhere between $100 and $1,000}. After that, you can buy as many bagels as desired at a cost of {use the GREEN slider to choose an amount – say anywhere between $0.00 and $2.00}.
The franchise fee to your donut supplier will be 40% that of your bagel supplier’s franchise fee. On the other hand, each donut will cost you 3 times as much as each bagel {use the BLUE slider to set the value}.
I. Using the values you have chosen
• Write a function that describes the total cost of buying a given number n of bagels.
• Write a function that describes the total cost of buying a given number n of donuts.
• Write an equation whose solution will tell you for what number of units the total cost of bagels is the same as the total cost of donuts
II. Solve your equation algebraically. Can you find this solution on the graphs? How does your solution depend on the franchise fee you pay? the cost of each unit?
III. Now pick a selling price {use the YELLOW slider}.
Using the values you have chosen
Write a function that describes the income you will derive from selling a given number n of either bagels or donuts. [Remember you can sell only one kind of breakfast food and the selling price of a bagel is the same as the selling price of a donut.]
Write a function that describes the profit you will make selling a given number n of bagels.
Write a function that describes the profit you will make selling a given number n of donuts
On the left side of the screen there are GREEN and BLUE bars that indicate “profit and loss”. How are they related to the graph?
What is the smallest number of each item that you would need to sell to have a profitable business? If you were expecting a small volume of sales, would you rather sell bagels, or donuts, or neither?
How many units of each item would you have to sell for the profit from the more profitable to be twice that of the less profitable?
[Adapted from Balanced Assessment in Mathematics Project - ©1995 President and Fellows of Harvard College]