A Sweet Volume: Designing a Jumbo Chocolate Bar Using Polynomials
Playing the role of engineers in collaborations with the marketing and production teams in a chocolate factory, students design a container for a jumbo chocolate bar. The projects constraints mean the container has to be a regular trapezoidal prism. The design has to optimize the material used to construct the container; that is, students have to find the dimensions of the container with the maximum volume possible. After students come up with their design, teams present a final version of the product that includes creative branding and presentation. The problem-solving portion of this project requires students to find a mathematical process to express the multiple variables in the prism’s volume formula as a single variable cubic polynomial function. Students then use technology to determine the value for which this function has a maximum and, with this value, find the prism’s optimal dimensions.
Receiving a giant chocolate bar as a gift is always a jolly surprise. Popular chocolate brands as Hershey’s or Toblerone produce jumbo versions of their products. Above are two funny ideas of homemade chocolate bar wrappers.Copyright 2019 Miguel R. Ramirez, Independent Contributor
Engineers are required to understand the concept of optimization to produce efficient and low-cost designs. They also need to maximize available materials or resources and perform optimization processes through the analysis of mathematical functions. Additionally, engineers use math functions such as polynomials in calculus and algebra in order to perform numerical analyses.
After this activity, students should be able to:
- Explain an optimization process in engineering design.
- Use the geometric net to build a regular prism and to express the variable prism’s volume formula as a single variable cubic polynomial function.
- Solve the graph of this polynomial to determine the value for which this function reaches a maximum, and with this value find the dimensions of the geometric net for the maximum volume possible.