At What Price?

1. At What Price? by Shermane King

2. The Cookie Problem "The Fresh Bakery currently sells 1000 large chocolate chip cookies each week for $0.50 each. The bakery would like to increase its revenue from the cookie sales by increasing this price. A survey convinced the manager that for every $0.10 increase, the bakery would sell 70 fewer cookies each week. At what price should the cookies be sold to maximize the revenue to the bakery?”

3. Initial Solution Algebra I: • Create a table • Create an equation for cookies, price and revenue: , , and (R = Cookies*Price) • Utilize that equations for the rest of the data and analyze the table to determine the price that will maximize revenue.

4. Solution!! Pre-Calculus • Know the equations for each:, , and • The revenue equation is a quadratic function • Graph the equation, which is a parabola • Find the vertex of the parabola which is d=65/14=4.64. • 4.64 represent the increase in dimes, so the cookie price is

5. Connection to Secondary Mathematics Algebra I: create a table, analyze table, generate solution. Algebra II: find the vertex of the parabola. Pre-Calculus: locate the vertex of the quadratic which is . Calculus: find first derivative and than solve for zero.

6. Extensions • Given revenue find the price and amount of cookies • Cost • Profit = revenue – cost • Change the problem completely

7. The End