This activity is designed to help students gain 3D visual intuition for the meaning of the Lagrange Multiplier approach to constrained optimization.  It is intended as an introduction to this topic to guide students through the discovery of the relationships involved.

See the PDFs for this activity here:
 212LA-Lagrange Multipliers Activity – Page 1
 212LA-LagrangeActivity-basepage – Page 2

For this activity we used a 3D-printed form along with a thermoformer to create the plastic surfaces.

Here is the Cura .3mf file for the surface whose contour plot is shown in the activity:

Cura .3mf file for the surface mold in a .zip file

Below you can see the Vaquform DT2 thermoformer that I used for this purpose in my office.