# PBL Pathways

##### Time Frame

2 to 3 weeks with mini-lectures

November 3, 2010

##### Keywords

marginal, demand, cost, revenue, profit, derivatives

Solar Toasters

#### Author

David Graser, Yavapai College, Prescott, AZ (David_Graser@yc.edu)

#### Abstract

In this project, students use pricing data for a product to come up with a linear demand function. From this function, students then form the corresponding revenue function, cost function and profit function. Finally, the derivative of the profit function, the marginal profit function, is computed and interpreted.

#### Project Content

Project Letter - DOC | PDF

#### Scaffolding Resources

Handout: How to Find a Revenue Function - DOC | PDF
Handout: Introduction to Revenue - PDF
Handout: Introduction to Cost -
PDF
Handout: Introduction to Break-Even
- PDF
Technology Assignment: Break-Even Point on the TI-84 and in Excel - PDF

#### Notes

The main issue students have with this project is scaling the units. If the number of toasters is scaled in hundreds, this automatically means that the revenue function is also scaled. If the cost function is not scaled similarly, they are bound to have trouble computing the profit function.

Students also have trouble distinguishing between profit and marginal profit.

I allow students to compute the derivative of the profit function from the definition of the derivative or with the power rule. My emphasis is on interpreting the marginal profit at 2000 units and what that means (ie. how procution should be changed).