*Maximum Cookies* is a Problem Based Learning unit that focuses on the use of graphs of linear inequalities to analyze and solve problems. The central unit problem involves a bakery that produces two kinds of cookies: plain and iced. The bakery faces constraints on ingredients, preparation time, and oven space. The two kinds of cookies require different amounts of ingredients and earn different amounts of profit. The task for students is to determine how many of each kind of cookie the bakery should produce to maximize overall profit.

**Driving Question**: How can we maximize profits for a small start-up business with limited resources?

Click on a link to jump ahead to the following sections:

- Unit Overview: Maximum Cookies
- Lesson 1 CW: "How Many of Each Kind?"
- Lesson 1 HW - A Simpler Cookie
- Lesson 2 - Investigating Inequalities
- Lesson 3 CW: My Simplest Inequality
- Lesson 3 HW - Simplifying Cookies
- Lesson 4a CW: Picturing Cookies, Part 1
- Lesson 4b CW: Inequality Stories (optional)
- Lesson 4 HW: Healthy Animals
- Lesson 5 CW: Picturing Cookies, Part 2
- Lesson 5 HW: What's My Inequality?
- Lesson 6: Feasible Diets
- Lesson 7: Picturing Pictures
- Lesson 7 CW: Profitable Pictures
- Lesson 8 HW: Curtis and Hassan Make Choices
- Lesson 9: Hassan's a Hit!
- Lesson 10 HW: You Are What You Eat
- Lesson 11 HW: Changing What You Eat
- Lesson 12 HW: Rock 'N' Rap
- Lesson 13: A Rock 'N' Rap Variation
- Lesson 14: "How Much of Each Kind" Revisited
- Lesson 15: Big State U
- Lesson 16: A Charity Rock
- Project: Business Plan
- Portfolio
**Culminating Project**: After students solve the unit problem, they will work in groups to create a web-based business plan for a small business of their choosing. Teams will publish on the internet a plan that analyzes the constraints of their business, designs a plan to optimize the profit, and justifies their optimization plan. View Business Plan details.**Supplemental Problems:**

The following are links to resources for Linear Programming, the topic being developed in the Maximum Cookies PBL:

- Linear Programming - Unit on Khan Academy

- Linear Programming lesson at Purplemath
- Video lesson on YouTube

- An example of a problem from the Math Forum's Ask Dr. Math

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