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 of 50 cents each. 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 a $200.00 initial payment to cover franchise fees and delivery costs for the rest of the school year. After that, you can buy as many bagels as desired at a cost of 12 cents per bagel. On the other hand, you can purchase donuts with no initial charge, at a cost of 30 cents each for the first 500 donuts, and 20 cents for each additional donut. Write a formula that describes the total cost of buying a given number of bagels, and another formula that describes the cost of buying a given number of donuts. Graph these two functions. Write another pair of functions that expresses the amount of profit (that is, the difference between your sales price and your expenses) from purchasing and selling each product. Explain in your own words what it would mean to have a negative profit. 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? (Remember that you're only allowed to sell one product.) Give evidence to support your findings. Suppose you project that you will be able to sell 2,000 items over the course of the year. Would you be better off selling bagels or donuts? How much better off? At what level of sales would a bagel business or a donut business be equally profitable? Guided by the above questions, describe a sales strategy for your business, detailing the costs involved and potential profits. Remember that the sales projection in question 5 is only an estimate; your work should address the potential impact of higher or lower sales. If you were allowed to sell both bagels and donuts, how would your business strategy change