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: 𝐶=1000−70𝑑 , 𝑃= 𝑑, and 𝑅=𝐶𝑃 (R = Cookies*Price)Utilize that equations for the rest of the data and analyze the table to determine the price that will maximize revenue.xcookiespricerevenue1000$$1930$$2860$$3790$$4720$$5650$$6580$$7510$$8440$$9370$$
4 Solution!! Pre-Calculus 𝑅=−7 4.64 2 +65 4.64 +500=650.89 Know the equations for each: 𝑃= 𝑑, 𝐷=1000−70𝑑, and 𝑅=𝑃𝐷The revenue equation is a quadratic function 𝑅(𝑑)=−7 𝑑 2 +65𝑑+500Graph the equation, which is a parabolaFind the vertex of the parabola which is d=65/14=18.104.22.168 represent the increase in dimes, so the cookie price is $0.50+$0.10∗4.64=$0.96𝑅=− =650.89
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 𝑦=𝑎𝑥²+𝑏𝑥+𝑐 which is ℎ= −𝑏 2𝑎 .Calculus: find first derivative and than solve for zero.
6 Extensions Given revenue find the price and amount of cookies Cost Profit = revenue – costChange the problem completely