木琴とヨーヨー: サンタの工房からのビジネス代数

Pre-Assignment:
The problem, involving choosing how much of two products to produce, will be posted in the classroom before the class meeting. Learners should familiarize themselves with the problem before the live session, and brainstorming some strategies is recommended. The expectation is not for learners to have completed the problem before class, but to have some ideas of how to start working on it, and maybe to have started some back-of-envelope scratch work.

During class:
We will use tables and graphs to identify which combinations of the two products are possible to produce. To use graphs, we will need to write inequalities for features of the problem which limit our production capabilities, called constraints.
We will use the given sales prices and production costs to write a profit function, then use this function to calculate the profit possible for different combinations of products. As we look for the maximum possible profit, we will try to find patterns to work efficiently.

Extension:
If learners complete the main problem quickly, this will be at least started during the session; otherwise the problem will be posted for learners to work on asynchronously. Learners will consider and form an opinion as to which of two options for increasing their production capacity would increase their profit more.

Learners will be more successful who are already familiar with evaluating formulas given values of variables, graphing linear inequalities, finding and verifying solutions to systems of linear equations, and the relationship in business between income, expenses, and profit. These concepts will be reviewed and discussed, but if many of them are new, the learner is likely to feel overwhelmed.