SUPPLEMENT: Linear Programming Application Day 2 of 2
Objective: SWBAT write inequalities using constraints, graph inequalities and identify a feasible region, write a profit function, and find maximum profit.
Big Idea: This lesson gives students the opportunity to synthesize what they have learned before they begin to create their own linear programming problems.
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Opening
I remind students that they are working on the Summer School Linear Programming Problem again today. The goal for this lesson is for students to finish their work on this problem and be ready to present it to the class.
Students began working on this problem in the previous lesson. I like to start the class by having them reflect on what worked well in their groups yesterday. This can help set the tone for a second productive day. I find that sometimes two days of group work in the same group can lead to some off track behavior or a loosening of classroom norms. So, the real purpose of this Lesson Beginning activity is to set the tone for the day’s work. Students could report out from their groups or I might have each student free write individually: what made their group successful on the previous day?
Investigation
At this point in the lesson, students will go back to their homogenous groups to continue their work. Students should have graphed the three inequalities and found the feasible region by the end of yesterday’s lesson (perhaps with some homework) and are ready to graph the profit line (or in this case, cost line).
Things I watch for:
- Students often struggle when they get to the profit line (or in this case, cost line) piece of the work. I remind them that they can choose any number of total costs that the school will spend. They may initially choose a number that is too small; I help them find a better line by encouraging them to choose a larger amount of cost. A number that works nicely for the cost line is $144,000.
As groups finish, I have them prepare presentations on this assignment.
