college algebra: the great cookie bake
College Algebra: The Great Cookie Bake Names: Date: Score: _/70 points scaled to _/30 points You are working with Student Government to generate funding for college activities. This year's big project is going to be a chocolate chip cookie bake and sale. In order to be successful, you will need to meet the profit goal of $900 to $1200, after all expenses are accounted for. You will need to solve the following problems in order to determine expenses, income, profits, and related issues. 1. After accounting for the cost of ingredients for an excellent chocolate chip cookie recipe, you arrive at the following cost relationship. The cost of (k) cookies will be 50.80 each plus a $275 fixed cost for rental of the kitchen and baking equipment. Write this as an equation, with the dependent variable C for cost, and the independent variable k for number of cookies made. (5) Write and solve an inequality to represent how many cookies you can make for up to $1000 in expenses. (5) 2. Past experience has helped you decide that you should charge $1.25 for each 3" diameter cookie. If Student Council already has been given a $225 donation to kick off the event, write an equation that you can use to determine the profit for cookies sold. The dependent variable S will represent total sales, while the dependent variable k will represent the number of cookies sold. (5) Write and solve an inequality to represent how many cookies you would need to sell in order for your total sales to exceed $1200. (5) 3. You really want to know what the break-even point" will be that is how many cookies will you need to make and sell in order for your Sales to be equal to your Costs. Anything sold over this amount will result in a profit! In order to find this number you will need to set the Cost and sales equations equal (Cost C = Sales S) and then solve for the number of cookies (k). (10) 4. What will be your total sales and cost) for this break-even" value? Check to see that both equations give you the same dollar amount. (4) 5. Now that you know how many cookies you need to break even, you can find how many you will need to generate a profit (P). Profit Pis equal to Sales S minus Cost Write the profit equation in simplified form using the equations from questions 1 and 2. 5. Now that you know how many cookies you need to break even, you can find how many you will need to generate a profit (P). Profit Pis equal to Sales S minus Cost C. Write the profit equation in simplified form using the equations from questions 1 and 2. (6) 6. Finally you will need to determine the range for the number of cookies you will need to sell in order to make a profit which is within the goal range of $900 to S1200. This will be a compound inequality of the form Here P" is the right-hand side of the equation from problem 5. (5) Solve the inequality to determine the range of the number of cookies you need to sell in order to meet your goal. (10) 7. Summarize your teams results by writing a short paragraph describing the process of finding cost, sales, and profit equations, what your break-even amount will be and how you determined the range of cookies you will need to make and sell in order to meet the Student Government goal. (15)
