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

**Abstract**

This project builds upon the Arsenic Removal from Drinking Water Group Project. In this project, students create a linear programming problem to describe how water from three wells can be combined to meet demand and meet arsenic and selenium standards. Each student uses a different level of contamination in Well 3 and then they work together to find which level is the very cheapest. The differences from the Arsenic Removal from Drinking Water Project are not always picked up by students and can lead to some very interesting discussions.

- Content Area – Finite Math
- Time Frame – 2 to 3 weeks with mini-lectures
- Published – June 22, 2015
- Keywords – linear programming

**Project Content**

**Scaffolding Resources**

**What is Parts per Million or Parts per Billion?** (PDF)

**Technology Assignment – Write Out a Standard Minimization Problem**

The goal of this assignment is to write the standard minimization problem for the project in a shared Google Doc.

The standard minimization problem they need to come up with will initially be a nonstandard form. Once they have the pieces of this linear programming problem, the team will need to convert the problem to standard form. The shared document should include a portion for the nonstandard form as well as the standard linear programming problem.

**Technology Assignment: Solve the Linear Programming Problem**

One of the most challenging parts of Finite Mathis carrying out the Simplex Method. The process is fairly straightforward, but is tedious and difficult to accomplish without arithmetic errors. In this assignment, each team member will carry out the Simplex Method with their level of contamination in Well 3. The video shows how to do the row operations within Google Sheets.

**Please note that there is a typo in the original matrix in the process above. The cell in D2 should be a 1 instead of a zero to account for the slack variable in the first constraint.**

Each team member should put their calculation in a shared Google Sheet in a separate tab. Do the row operations as indicated in the video.

Once the team has completed this assignment, they can compare the lowest cost from each team member to determine which contamination level yield the very lowest cost.

**Notes**

- Demanding that at least a certain amount of water is produced impacts more than just one constraint. This is the biggest hurdle students need to overcome.